Question

A ball is thrown straight out at 80 feet per second from an upstairs window that's 15 feet off the ground. It turns out that its motion can be broken down into its motion in the x-direction (horizontally) and its motion in the y-direction (vertically), and that those two components can be thought of completely independently. In other words, its horizontal motion has no influence on its vertical motion, and vice versa. I've written the two component functions here: x(t) is its position in the x-direction, and y(t) is its position in the y-direction. Which of the following choices is correct? (Ignore air resistance.) NOTE: Use a reference frame that makes all positions (x and y coordinates) of the projectile positive.

Answer 1

Answer:

Step-by-step explanation:

Given that ball is thrown vertically with intial velocity 80 ft per second at a height of 15 feet off the ground.

Let angle of the ball thrown with horizontal be A

Then vertical velocity = 80 sinA

HOrizontal velocity = 80 cosA

Acceleration here is negative gravity

In fps system gravity g = -32ft/sec^2

s=ut+1/2at^2

Substitute to get

h(t) = 80cos A  t-16t^2 +15 (since initial height is 15 ft)

x(t) = 80 sin A t

Answer 2

$x(t) = 80t \\ \\ y(t) = -16t^2 + 15$