Question

In a desperate attempt to get Juliet's attention, Romeo (who is 6 foot tall) throws a rock from 1 foot above his head at an angle of 45° with a velocity of 22 meters per second. Assuming that the rock hits the center of the window when it has reached it's highest point, how high is the window (the center of the window, in meters)? a. 24.7 b. 12.4 c. 26.8 D14.5 e. None ofThese 7. If Juliet, who just caught a glimpse of Romeo picking up the rock, excitedly ran to the window and opened it 2 seconds after Romeo threw the rock, would the rock hit the window or Juliet? aThe Window b. Juliet

Answer 1

We can use kinematic equations to solve this problem. The initial vertical velocity of the rock is given by v0y = v0 * sin(45) = 22 * sin(45) = 15.6 m/s, where v0 is the initial velocity of the rock. The maximum height of the rock is reached when its vertical velocity is zero. Using the kinematic equation vf^2 = v0^2 + 2 * a * d, where vf is the final velocity, v0 is the initial velocity, a is the acceleration, and d is the distance traveled, we can solve for the maximum height reached by the rock. Plugging in the values we have and solving for d, we get:

0 = 15.6^2 + 2 * (-9.8) * d d = 15.6^2 / (2 * 9.8) ≈ 12.4

Since Romeo threw the rock from 1 foot above his head and he is 6 feet tall, the initial height of the rock was 6 + 1 = 7 feet or approximately 2.13 meters above the ground. Therefore, the center of the window is at a height of approximately 12.4 + 2.13 = 14.53 meters above the ground.

To answer your second question, we can use another kinematic equation to find out how high the rock would be after 2 seconds. The equation is d = v0t + (1/2)at^2, where d is the distance traveled, v0 is the initial velocity, t is time and a is acceleration. Plugging in the values we have and solving for d, we get:

d = 15.6 * 2 + (1/2) * (-9.8) * 2^2 ≈ 17.6

So after 2 seconds, the rock would be approximately 17.6 meters above its initial position or approximately 17.6 + 2.13 = 19.73 meters above the ground.

Since this height is higher than the center of the window (14.53 meters), it means that the rock would hit Juliet if she opened the window after 2 seconds.