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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:
- The initial velocity of the ball is +u m/s.
- As the ball rises, its velocity decreases due to gravity until it reaches zero at the peak height, which occurs at 2 seconds.
- After reaching its peak, the velocity becomes negative as the ball descends back down.
The graph should show:
- A straight line from (0, u) to (2, 0) (where the ball reaches its maximum height) and then back down from (2, 0) to (4, -u). The graph will look like a V shape, where the peak occurs at 2 seconds.
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
To find the value of u, we can use the kinematic equation for the maximum height:
where:
- h = 19.6 m (the maximum height)
- u = initial velocity (unknown)
- t = time to reach maximum height = 2 s
- a = acceleration due to gravity = -9.8 m/s² (negative as it's acting downward)
Plugging in the values:
This simplifies to:
Adding 19.6 to both sides gives:
Dividing by 2, we find: