Question

HELP ME PLEASE I DONT UNDERSTAND THIS PROBLEM!!!!! Worth 20PT

a ball is thrown with a slingshot at a velocity of 100 ft/sec at an angle 21 above the ground from a height of 5ft approximately how long does it take for the ball to hit the ground? acceleration due to gravity is 32 ft/s^2

Answer 1

D) 2.37 seconds

Explanation:

Took the test and got it wrong.

Answer 2

It takes approximately 6.3 seconds to hit the ground.

We use the equation h(t)=-1/2gt²+v₀t+h₀ to set this up. g is the acceleration due to gravity, v₀ is the initial velocity and h₀ is the initial height:
h(t) = -1/2(32)t² + 100t + 5
h(t) = -16t² + 100t + 5

We will use the quadratic formula to solve this:

`t=(-b\pm√(b^2-4ac))/(2a) \\ \\=(-100\pm√(100^2-4(-16)(5)))/(2(-16)) \\ \\=(-100\pm√(10000--320))/(-32) \\ \\=(-100\pm√(10320))/(-32) \\ \\=(-100\pm101.59)/(-32) \\ \\=(-100+101.59)/(-32)\text{ or }(-100-101.59)/(-32) \\ \\=(1.59)/(-32)\text{ or }(-201.59)/(-32) \\ \\=-0.05\text{ or }6.3`

Since a negative amount of time makes no sense, the answer is 6.3.