A young man is throwing rocks gently up to his girlfriend's window, and he wants the rocks to hit the window moving only with a horizontal component of velocity. He is standing at the edge of a flower bed h = 7.9 m below her window and d = 9.0 m from the base of the wall (see figure). How fast are the rocks going when they hit her window?
Since it takes the same time to rise as it does to fall, how long does it take to fall 7.9 meters?
4.9t^2 = 7.9
Use that value of t to see how fast (horizontally) you have to move to cover 9 meters in that time.
v = 9/t
To find the velocity of the rocks when they hit the window, we need to consider the laws of physics and use the concept of projectile motion.
In this scenario, the rocks are being thrown with a horizontal component of velocity and will follow a parabolic trajectory due to gravity. The vertical distance h between the flower bed and the window will influence the time it takes for the rocks to travel horizontally.
To solve this problem, we can break it down into two components: horizontal and vertical.
1. Horizontal Motion:
Since the rocks have only a horizontal component of velocity, the horizontal motion is constant. The horizontal distance d from the base of the wall to the young man is given as 9.0 m. Therefore, the horizontal component of velocity (Vx) remains constant throughout the motion, and its value can be found by using the equation:
Vx = d / t
Here, t represents the time taken for the rocks to reach the window.
2. Vertical Motion:
The vertical motion is affected by gravity. The vertical distance h from the flower bed to the window is given as 7.9 m. We can calculate the time it takes for the rocks to fall from this height using the equation of motion:
h = (1/2) * g * t^2
Here, g represents the acceleration due to gravity, which is approximately equal to 9.8 m/s^2.
Solving this equation for t, we get:
t = sqrt(2 * h / g)
Now that we have the value of t, we can substitute it back into the equation from horizontal motion to find the horizontal component of velocity (Vx).
Vx = d / t
And lastly, to find the overall velocity (V), we can use the Pythagorean theorem, as the horizontal and vertical components are perpendicular to each other:
V = sqrt(Vx^2 + Vy^2)
Since the rocks only have a horizontal component of velocity, Vy (vertical component of velocity) is equal to 0.
Therefore, the overall velocity of the rocks when they hit the window will be equal to the horizontal component of velocity (Vx).
To summarize, follow these steps to find the answer:
1. Calculate the time taken for the rocks to fall using t = sqrt(2 * h / g).
2. Substitute the value of t into the equation Vx = d / t to find the horizontal component of velocity (Vx).
3. The velocity of the rocks when they hit the window will be equal to the horizontal component of velocity (Vx).