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

Answer:

1) 1.1 seconds

2) 13.5 feet

Part A

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

Apply quadratic formula:

$\rightarrow \sf t= \dfrac{-5\pm \sqrt{5^2-4\left(-16\right)\cdot \:15}}{2\left(-16\right)}$

Simplify following

$\rightarrow \sf t=-\dfrac{-5+\sqrt{985}}{32},\:t=\dfrac{5+\sqrt{985}}{32}$

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

$\rightarrow \sf h=13.5$