Physics Practice Problems Projectile Motion: Positive Launch Practice Problems Solution: In the long jump, an athlete launches herself at a...

Solution: In the long jump, an athlete launches herself at an angle above the ground and lands at the same height, trying to travel the greatest horizontal distance. Suppose that on earth she is in the air for time t, reaches a maximum height h, and achieves a horizontal distance D.If she jumped in exactly the same way during a competition on Mars, where gMars is 0.379 of its earth value, find her...(a) time in the air.(b) maximum height.(c) horizontal distance.

Problem

In the long jump, an athlete launches herself at an angle above the ground and lands at the same height, trying to travel the greatest horizontal distance. Suppose that on earth she is in the air for time t, reaches a maximum height h, and achieves a horizontal distance D.

If she jumped in exactly the same way during a competition on Mars, where gMars is 0.379 of its earth value, find her...

(a) time in the air.

(b) maximum height.

(c) horizontal distance.

Solution

This problem requires us to determine the time in the air, maximum height, and the horizontal distance (range) when the gravitational acceleration is changed.

Since the takeoff and landing are at the same height, this is a symmetrical launch problem.

For projectile motion problems in general, we'll follow these steps to solve:

  1. Identify the target variable and known variables for each direction—remember that only 3 of the 5 variablesx or Δy, v0, vf, a, and t) are needed for each direction. Also, it always helps to sketch out the problem and label all your known information!
  2. Choose a UAM equation—sometimes you'll be able to go directly for the target variable, sometimes another step will be needed in between.
  3. Solve the equation for the target (or intermediate) variable, then substitute known values and calculate the answer.

In step 2, for the special case of a symmetrical launch, we also have equations for the time in air, horizontal distance traveled, also called the range, and maximum height of the projectile:

t=2v0gsin θ, R=v02 sin(2θ)g  and   Hmax=v02 sin2θ2g

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