A circus performer throws an apple toward a hoop held by a performer on a platform (see figure below). The thrower aims for the hoop and throws with a speed of 22 m/s. At the exact moment the thrower releases the apple, the other performer drops the hoop. The hoop falls straight down. (Assume

d = 31 m and h = 52 m.
Neglect the height at which the apple is thrown.)At what height above the ground does the apple go through the hoop? the answer key is 14.9m but I don't know how to get there nor which equation to use for this problem

what is d, and what is h?

I think d is the distance and h is the height

is there anyway for I to send you the figure so you know what is d and h. Once you srr the figure you will understand

To solve this problem, we can use the equations of motion and consider both vertical and horizontal motion separately.

Let's start with the vertical motion of the apple. We can use the equation:

h = h0 + v0*t - (1/2)*g*t^2

Where:
h is the height above the ground at any time t,
h0 is the initial height (which is 0 in this case, since we are measuring heights above the ground),
v0 is the initial vertical velocity (which is 0 in this case as well, since the apple is thrown horizontally),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
t is the time.

We can rearrange this equation to solve for t:

t = (√(2*h/g))

Now, let's consider the horizontal motion of the apple. Since no horizontal forces act on the apple, it travels with a constant horizontal velocity. The horizontal displacement can be calculated as:

d = v0*t

Since v0 is the horizontal velocity, which is equal to the initial speed of 22 m/s, we can substitute t from the equation above into the equation for horizontal displacement:

d = 22*(√(2*h/g))

We can rearrange this equation to solve for h:

h = (d^2*g)/(2*(22^2))

Now we can substitute the given values into this equation to find the height above the ground where the apple goes through the hoop:

h = (31^2 * 9.8)/(2*(22^2))
h ≈ 14.9 m

Therefore, the height above the ground where the apple goes through the hoop is approximately 14.9 meters.