Answer to Question #154366 in Algebra for Kinza Tahir

Question

A golf ball is hit from the ground and can be represented by the equations h= - 3t2+10t or h=t(-3t+10) where h is the height in meters and t is the time in seconds.

a) Determine how long the golf ball was in the air.

b) Determine at what time the golf ball reached its maximum height.

c) Determine the maximum height of the golf ball.

Answer 1

a) $h=0=>t(-3t+10)=0$

$$t_1=0, t_2=\dfrac{10}{3}$$

The golf ball was in the air $\dfrac{10}{3}$ seconds.

b) $h(t)=-3t^2+10t$

$$t_{m}=-\dfrac{10}{2(-3)}=\dfrac{5}{3}$$

The golf ball reached its maximum height $\dfrac{5}{3}$ seconds after start.

c)

$$h(\dfrac{5}{3})=\dfrac{5}{3}(-3(\dfrac{5}{3})+10)=\dfrac{25}{3}$$

The maximum height of the golf ball is $\dfrac{25}{3}$ meters above the ground.