Answer:
Time in air = 2.26 seconds
Explanation:
Time in air is the sum of the time taken to reach maximum height and the time taken to hit the ground from maximum height.
i.e
Time in air = Time to reach max. height + Time to hit the ground from max. height
<u>Calculate time to reach max height</u>
Using one of the equations of motion;
v = u + at
where;
v = final velocity at max. height = 0 (at max. height, final velocity is zero)
u = initial velocity = 16.0m/s
a = acceleration due to gravity = -g (since the ball moves up against gravity)
t = time taken
Substitute the values of v, u and a into the equation above;
0 = 16 - gt
Taking g as 10, we have;
0 = 16 -10t
Making t subject of the formula;
t = 16 / 10 = 1.6 s
Therefore, time taken to reach max. height is 1.6 seconds
<u>Calculate time to hit ground from max. height</u>
First calculate the max. height reached using the equation;
h = ut + a
where;
h is the height
u = initial velocity = 16m/s
a = acceleration due to gravity = -g (since the ball moves up against gravity)
t = time taken to reach max. height = 1.6s
Substitute the values of u, a and t into the equation above;
h = 16x1.6 - x g x
Taking g as 10, we have;
h = 16x1.6 - x 10 x
h = 25.6 - 12.8
h = 12.8m
Remember that the ball was thrown at a height of 2.50mm above the ground;
Therefore, total height reached = 12.8m + 2.50mm
Convert 2.50mm to m we have
=> 2.50mm = 0.0025m
Total height reached = 12.8 + 0.0025 = 12.8025m
Now calculate the time taken to hit the ground using the same equation;
h = ut + a
where;
h is the total height reached = 12.8025m
u = initial velocity = 16m/s
a = acceleration due to gravity = +g (since the ball now moves downwards in the direction of gravity)
t = time taken to hit the ground
Substitute the values of u, a and t into the equation above;
12.8025 = 16xt + x g x
Taking g as 10, we have;
12.8025 = 16xt + x 10 x
12.8025 = 16t + 5
Rearranging;
5 + 16t - 12.8205 = 0
Solving the quadratic equation gives;
t = 0.66 or t = -3.86
Since time cannot be negative, t = 0.66s
Therefore time taken to hit the ground is 0.66s
<u>Calculate time in air</u>
Time in air = Time to reach max. height + Time to hit the ground from max. height.
Time in air = 1.60 + 0.66
Time in air = 2.26seconds
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<em>Note: I'd imagine that the ball left the student's hand with when the hand was </em><em>2.50m</em><em> above the ground and </em><em>not 2.50mm</em><em>. But then, i have followed what was typed. I have stuck to 2.50mm.</em>
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