Question

A soccer player kicks a ball with an initial velocity of 35 feet per second from a starting point of 0 feet. Use the equation h(t)=-16t^2+bt+c, where v is the initial velocity in feet/second and c is the height in feet. Round to the nearest tenth.

#1 Calculate how long the ball was in the air
#2 Calculate the maximum height of the ball

Please help asap

Answer 1

2.2 seconds

Explanation:

h(t)=-16t^2+bt+c

We know the initial velocity is 35 = b

We know the initial height is 0 =c

h(t)=-16t^2+35t+0

h(t)=-16t^2+35t

Question 1 is to find when the ball hits the ground or when h(t) is 0

0=-16t^2+35t

Factor out a t

0 = t( -16t+35)

We can use the zero product property to solve for t

t=0 -16t+35 =0

Subtract 35 from each side

-16t = -35

Divide by -16

-16t/-16 = -35/-16

t = 2.1875 seconds

t=0 is when the ball is kicked

t =2.1875 is when the ball lands on the ground after being kicked

Rounded to the nearest tenth

2.2 seconds

19.1 ft

The maximum height is at the axis of symmetry

h = -b/2a

-35/(2*-16)

-35/-32

35/32

This is the t value

To find the maximum height , we need to put this in the equation to find the y value

h(35/32) = -16( 35/32)^2 + 35 *(35/32)

= -16* 1.196289 +38.28125

19.140625 ft

Rounding to the nearest tenth

19.1 ft