Question

2. Mourette is a member of her high school golf team. She hits a golf ball

off the ground with an initial upward velocity of 60 meters per second.
a. Write a formula describing the height h of the ball (in meters)
after t seconds.
b. After how many seconds, to the nearest tenth, will the
golf ball land on the ground?
c. What is the maximum height the golf ball reaches?

please help!

Answer 1

a. h = 60t − 4.9t²

b. 12.2 seconds

c. 183.7 meters

Explanation:

a. Given:

y₀ = 0 m

v₀ = 60 m/s

a = -9.8 m/s²

y = y₀ + v₀ t + ½ at²

h = 0 m + (60 m/s) t + ½ (-9.8 m/s²) t²

h = 60t − 4.9t²

b. When the ball lands, h = 0.

0 = 60t − 4.9t²

0 = t (60 − 4.9t)

t = 0 or 12.2

The ball lands after 12.2 seconds.

c. The maximum height is at the vertex of the parabola.

t = -b / (2a)

t = -60 / (2 × -4.9)

t = 6.1 seconds

Alternatively, the maximum height is reached at half the time it takes to land.

t = 12.2 / 2

t = 6.1 seconds

After 6.1 seconds, the height reached is:

h = 60 (6.1) − 4.9 (6.1)²

h = 183.7 meters