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Sindrei [870]
3 years ago
15

A ball is thrown straight down from the top of a building at a velocity of 16 ft/s. The building is 480 feet tall, and the accel

eration due to gravity is 32 ft/s2.
This problem can be represented using the following equation.

How much time will the ball take to reach the ground? (1/2)32t^2+16t=480
Mathematics
1 answer:
Doss [256]3 years ago
5 0

Answer:

Time, t = 5 seconds.

Step-by-step explanation:

<u>Given the following data;</u>

Initial velocity = 16 ft/s

Height = 480 ft

Acceleration due to gravity = 32 ft/s²

To find how much time it will take the ball to reach the ground, we would use the kinematic equation given by the formula;

d = V_{i}t + \frac {1}{2}at^{2}

Where;

  • d is the displacement.
  • Vi is the initial velocity.
  • a is the acceleration or acceleration due to gravity.
  • t is the time measured in seconds.

Substituting into the equation, we have;

480 = 16t + \frac {1}{2}*32t^{2}

480 = 16t + 16t^{2}

Dividing all through by 16, we have;

30 = t + t^{2}

Re-arranging the quadratic equation, we have;

t^{2} + t - 30 = 0

We would solve the quadratic equation by factorization;

t^{2} + 6t - 5t - 30 = 0

t(t + 6) - 5(t + 6) = 0

(t + 6)(t - 5) = 0

t = -6 or 5

Since we know time can't be negative, we would ignore the value of -6.

<em>Therefore, time = 5 seconds</em>

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