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A small ball is projected vertically upwards from ground level with speed u m s⁻¹ - Edexcel - A-Level Maths Mechanics - Question 2 - 2009 - Paper 1
Question 2
A small ball is projected vertically upwards from ground level with speed u m s⁻¹. The ball takes 4 s to return to ground level. (a) Draw, in the space below, a vel... show full transcript
Worked Solution & Example Answer:A small ball is projected vertically upwards from ground level with speed u m s⁻¹ - Edexcel - A-Level Maths Mechanics - Question 2 - 2009 - Paper 1
Step 1
Draw, in the space below, a velocity-time graph to represent the motion of the ball during the first 4 s.
Answer
To draw the velocity-time graph:
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Start at the initial velocity, which is equal to the speed 'u' m/s.
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As the ball rises, the velocity decreases uniformly due to the effect of gravity until it reaches 0 m/s at its maximum height, which occurs at 2 seconds (half of the total time of 4 seconds).
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From the maximum height, the ball descends, and its velocity increases negatively (downward) back to -u m/s at 4 seconds.
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The graph will be a straight line that slopes downward from (0, u) to (2, 0) and then slopes upward from (2, 0) to (4, -u).
Step 2
The maximum height of the ball above the ground during the first 4 s is 19.6 m. Find the value of u.
Answer
Using the kinematic equation for vertical motion,
where:
- s = maximum height (19.6 m)
- u = initial velocity (to be found)
- a = acceleration due to gravity (-9.8 m/s², acting downward)
- t = time to reach maximum height (2 s)
Substituting the values:
This simplifies to:
Add 19.6 to both sides:
Dividing both sides by 2 gives: