Question

Bryan shoots a rock up in the air with his slingshot . Initially the rock is at rest when the slingshot is pulled back but as the sling is released the rock is accelerating up at 82 m/s^2 until it leaves the slingshot after .091 seconds at 35 cm above Bryan’s head. After it has left the slingshot, the rock continues to move upward until it reaches its maximum height before running towards the ground. How long would Bryan have to move out of the way before he was hit in the head by the rock?

Answer 1

Bryan would have to move out of the way within 0.091 seconds after the rock leaves the slingshot to avoid getting hit in the head.

Step-by-step explanation:

To calculate how long Bryan would have to move out of the way before he was hit in the head by the rock, we need to find the time it takes for the rock to reach its maximum height after leaving the slingshot. We can use the equation for motion under constant acceleration: vf = vi + at. Since the rock is moving upwards, its final velocity at the maximum height is 0 m/s.

The initial velocity is given as 82 m/s² and the acceleration is also given as 82 m/s². Rearranging the equation, we have 0 = 82t + 82(0.091). Solving for t, we find that t = -0.091 seconds. Since time cannot be negative, we take the positive value: t = 0.091 seconds.

Therefore, Bryan would have to move out of the way within 0.091 seconds after the rock leaves the slingshot to avoid getting hit in the head.