h(t) = -0.81t^2 + 5t. What is the maximum height of the ball? How long is it in the air for?

Question

anonymous · Answer

You are an astronaut on the Moon. You hit a golf ball with your golf club. The height of the ball, h(t), in metres, after time, t, is modeled by the function h(t) = -0.81t^2 + 5t. What is the maximum height of the ball? How long is it in the air for?

nincompoop · Answer

maximum height, set equation to velocity = 0

nincompoop · Answer

or algebraically, you can use the vertex formula to obtain the height

campbell_st · Answer

well for this question the max height occurs on the line of symmetry.... 

so use 

for any quadratic, 

$$at^2 + bt + c = 0$$

$$t = \frac{-b}{2a}$$

in your question a = -0.81, then the b value is 5

when you get t, this is the time the max height occurs, substitute it into the original equation to find the max height. 

now time of flight

the flight stops when the height = 0  so h(t) = 0

just solve 

$$0 = -0.81t^2 + 5t$$

so the flight starts at time t = 0 and finishes at the other answer for t. 

hope it helps

anonymous · Answer

thanks so much campbell!

nincompoop · Answer

it was exactly what I said

anonymous · Answer

you told me what i needed to do , which i already knew. I needed help with how to do it, step by step.