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iren [92.7K]
3 years ago
15

A man throws a ball into the air with a velocity of 96 ft/s. Use the formula h=−16 t 2 + v 0 t to determine when the height of t

he ball will be 48 feet. Round to the nearest tenth.
Mathematics
2 answers:
Kay [80]3 years ago
8 0

Answer:

t=5.4 and t=0.6.

Step-by-step explanation:

The height of the ball (in feet) after time t is defined by the function

h=-16t^2+v_0t

where, v_0 is initial velocity.

It is given that a man throws a ball into the air with a velocity of 96 ft/s.

Substitute v=96 in the above function.

h=-16t^2+96t

We need to find the time at which the height of ball is 48 feet.

48=-16t^2+96t

16t^2-96t+48=0      .... (1)

Quadratic formula for ax^2+bx+c=0 is

x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

In equation a=16, b=-96 and c=48. Using quadratic formula we get

t=\dfrac{-(-96)\pm \sqrt{(-96)^2-4(16)(48)}}{2(16)}

t=\dfrac{96\pm \sqrt{9216-3072}}{32}

t=\dfrac{96\pm 78.384}{32}

t=\dfrac{96+78.384}{32} and t=\dfrac{96-78.384}{32}

t=5.449 and t=0.55

Round the answer to the nearest tenth.

t\approx 5.4 and t\approx 0.6

Therefore, the height of ball will be 48 feet at t=5.4 and t=0.6.

Ann [662]3 years ago
6 0

Answer:

Assuming that v0 represents the initial velocity, then v0 = 96 ft/s. Substitute this value into h(t) and set the equation equal to 48. Then, write this quadratic equation in standard form, which is ax² + bx+ c = 0, where a, b, and c are constants. Either use factoring or the Quadratic Function to solve the equation for t. Remember that t must be positive, because it represents a unit of time.

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