Question

Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. when sharon jumps, megan throws a beach ball up to sharon with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. to the nearest hundredth of a second, how long after she jumps does the ball reach sharon? 0.65 seconds 0.92 seconds 1.08 seconds 1.15 seconds

Answer 1

It will take 1.08 seconds for the ball to reach Sharon after she jumps if the upward velocity of the ball is 16 ft/s from a height of 5 feet option third is correct.

What is the equation of motion?

It is defined as the equation by which we can find the motion of a physical particle with respect to time. It is the representation of physical entity movement in a mathematical function.

We have:

The height of the Sharon from the diving board = 18 feet

The initial upward velocity of the Sharon = 4 ft/s

The height of the Megan from the ground = 5 feet

The initial upward velocity of the beach ball = 16 ft/s

We know the equation of motion is given by:

$\rm h(t) = x + ut+\frac{1}{2} gt^2$

Put x = 18 feet and u = 4 ft/s in the above equation, we get:

$\rm h(t) = 18 + 4t+\frac{1}{2} \times9.8t^2$ ....(1)     [g = 9.8 m/s²]

Put x = 5 feet and u = 16 ft/s in the equation of motion, we get:

$\rm h(t) = 5 + 16t+\frac{1}{2} \times9.8t^2$  ....(2)

Equate the equation (1) and equation (2), we get

$\rm 18 + 4t+\frac{1}{2} \times9.8t^2= 5 + 16t+\frac{1}{2} \times9.8t^2$

18 + 4t = 5 + 16t

12t = 13

t = 1.08 seconds

Thus, it will take 1.08 seconds for the ball to reach Sharon after she jumps if the upward velocity of the ball is 16 ft/s from a height of 5 feet.

Learn more about the equation of the motion here:

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