Question

A ball is thrown upward from a height of 15 ft with an initial velocity of 5 ft/s. Use the equation h=-16t^2+5t+15 to answer the following questions. Round to the nearest tenth.

How long will it take for the ball to hit the ground (h=0)?


What is the height of the ball after 0.5 seconds?​

Answer 1

1) 1.1 seconds

2) 13.5 feet

Part A

`\rightarrow \sf -16t^2 + 5t + 15 = 0`

Apply quadratic formula:

`\rightarrow \sf t= (-5\pm √(5^2-4\left(-16\right)\cdot \:15))/(2\left(-16\right))`

Simplify following

`\rightarrow \sf t=-(-5+√(985))/(32),\:t=(5+√(985))/(32)`

In decimal form:

`\rightarrow \sf t=-0.825 ,\:t=1.137`

Conclusion:

As time is be only positive: t = 1.1 seconds

Part B

`\rightarrow \sf h=-16t^2 + 5t + 15`

insert t = 0.5

`\rightarrow \sf h=-16(0.5)^2 + 5(0.5) + 15`

simplify

`\rightarrow \sf h=13.5`