How fast must a projectile moving

As the projectile rises towards its peak, it is slowing down Finally, the symmetrical nature of the projectile's motion can be seen in the diagram above: the vertical speed one second before reaching its peak is the same as the vertical speed one second after falling from its peak. The vertical speed two seconds before reaching its peak is the same as the vertical speed two seconds after falling from its peak. These concepts are further illustrated by the diagram below for a non-horizontally launched projectile that lands at the same height as which it is launched.

Sanders' Site. What is a Projectile? Projectile Motion and Inertia Many students have difficulty with the concept that the only force acting upon an upward moving projectile is gravity. Describing Projectiles With Numbers: Horizontal and Vertical Velocity A projectile is any object upon which the only force is gravity, Projectiles travel with a parabolic trajectory due to the influence of gravity, There are no horizontal forces acting upon projectiles and thus no horizontal acceleration, The horizontal velocity of a projectile is constant a never changing in value , There is a vertical acceleration caused by gravity; its value is 9.

Time Horizontal Velocity Vertical Velocity 0 s My Resources. Classroom News. My Homework. My Calendar. Kinematic Equations. Newtons 3rd Law. Notes on Acceleration Graphs.

Notes on Forces. Notes on Newtons 1st Law. Notes on Newtons 2nd Law. Notes on Vectors. Notes on Velocity Graphs. Types of Forces. Notes on Inclined Planes. Projectile Motion Notes. Notes on Momentum and Impulse. Circular Motion. Universal Law of Gravitation. Energy in a Closed System. Notes on Springs. Energy in an Open System. Sound Waves Notes. When solving Figure a , the expression we found for y is valid for any projectile motion when air resistance is negligible.

This equation defines the maximum height of a projectile above its launch position and it depends only on the vertical component of the initial velocity. On its way down, the ball is caught by a spectator 10 m above the point where the ball was hit. Again, resolving this two-dimensional motion into two independent one-dimensional motions allows us to solve for the desired quantities.

The time a projectile is in the air is governed by its vertical motion alone. Thus, we solve for t first. While the ball is rising and falling vertically, the horizontal motion continues at a constant velocity. This example asks for the final velocity. Thus, we recombine the vertical and horizontal results to obtain.

We can find the time for this by using Figure :. The initial vertical velocity is the vertical component of the initial velocity:. Substituting into Figure for y gives us. Since the ball is at a height of 10 m at two times during its trajectory—once on the way up and once on the way down—we take the longer solution for the time it takes the ball to reach the spectator:.

The time for projectile motion is determined completely by the vertical motion. Thus, any projectile that has an initial vertical velocity of Then, we can combine them to find the magnitude of the total velocity vector.

We choose the starting point because we know both the initial velocity and the initial angle. The final vertical velocity is given by Figure :. This result is consistent with the fact that the ball is impacting at a point on the other side of the apex of the trajectory and therefore has a negative y component of the velocity.

The magnitude of the velocity is less than the magnitude of the initial velocity we expect since it is impacting Of interest are the time of flight, trajectory, and range for a projectile launched on a flat horizontal surface and impacting on the same surface.

In this case, kinematic equations give useful expressions for these quantities, which are derived in the following sections. We can solve for the time of flight of a projectile that is both launched and impacts on a flat horizontal surface by performing some manipulations of the kinematic equations.

We note the position and displacement in y must be zero at launch and at impact on an even surface. Thus, we set the displacement in y equal to zero and find. This is the time of flight for a projectile both launched and impacting on a flat horizontal surface. Figure does not apply when the projectile lands at a different elevation than it was launched, as we saw in Figure of the tennis player hitting the ball into the stands.

The time of flight is linearly proportional to the initial velocity in the y direction and inversely proportional to g. Thus, on the Moon, where gravity is one-sixth that of Earth, a projectile launched with the same velocity as on Earth would be airborne six times as long.

The trajectory of a projectile can be found by eliminating the time variable t from the kinematic equations for arbitrary t and solving for y x. We take. Substituting the expression for t into the equation for the position. From the trajectory equation we can also find the range , or the horizontal distance traveled by the projectile. Factoring Figure , we have. The position y is zero for both the launch point and the impact point, since we are again considering only a flat horizontal surface.

Note particularly that Figure is valid only for launch and impact on a horizontal surface. We see the range is directly proportional to the square of the initial speed. Thus, on the Moon, the range would be six times greater than on Earth for the same initial velocity.

Furthermore, we see from the factor. These results are shown in Figure. In a we see that the greater the initial velocity, the greater the range. In b , we see that the range is maximum at. This is true only for conditions neglecting air resistance. If air resistance is considered, the maximum angle is somewhat smaller. It is interesting that the same range is found for two initial launch angles that sum to. The projectile launched with the smaller angle has a lower apex than the higher angle, but they both have the same range.

Note that the range is the same for initial angles of. Example Comparing Golf Shots A golfer finds himself in two different situations on different holes. On the second hole he is m from the green and wants to hit the ball 90 m and let it run onto the green. He angles the shot low to the ground at. On the fourth hole he is 90 m from the green and wants to let the ball drop with a minimum amount of rolling after impact.

Here, he angles the shot at. Both shots are hit and impacted on a level surface. The horizontal motion of the falling flare remains constant, and as such, the flare will always be positioned directly above the snowmobile. The force of gravity causes the flare to slow down and then return to the ground; yet it does not affect the horizontal motion of the flare. Suppose a rescue airplane drops a relief package while it is moving with a constant horizontal speed at an elevated height.

Assuming that air resistance is negligible, where will the relief package land relative to the plane? The package will land directly below the plane. The horizontal motion of the falling package remains constant, and as such, the package will always be positioned directly below the plane.

The force of gravity causes the package to fall but does not affect its horizontal motion. Physics Tutorial. My Cart Subscription Selection. Student Extras. What is a Projectile? We Would Like to Suggest Sometimes it isn't enough to just read about it. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives.

We would like to suggest that you combine the reading of this page with the use of our Projectile Motion Simulator.

If you were to look out horizontally along the horizon of the Earth for meters, you would observe that the Earth curves downwards below this straight-line path a distance of 5 meters. In order for a satellite to successfully orbit the Earth, it must travel a horizontal distance of meters before falling a vertical distance of 5 meters. A horizontally launched projectile falls a vertical distance of 5 meters in its first second of motion.

When launched at this speed, the projectile will fall towards the Earth with a trajectory which matches the curvature of the Earth. As such, the projectile will fall around the Earth, always accelerating towards it under the influence of gravity, yet never colliding into it since the Earth is constantly curving at the same rate. Such a projectile is an orbiting satellite. To further understanding the concept of a projectile orbiting around the Earth, consider the following thought experiment.

Suppose that a very powerful cannon was mounted on top of a very tall mountain. Suppose that the mountain was so tall that any object set in motion from the mountaintop would be unaffected by air drag.