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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 represent the motion of the ball, the velocity-time graph will have the following characteristics:
- Initial Velocity (u): The graph begins at a positive velocity
um/s, when the ball is projected upwards. - Velocity decreases to 0: The graph slopes downward reaching a velocity of
0att = 2s, the moment when the ball reaches its maximum height. - Velocity becomes negative: From
t = 2s tot = 4s, the ball returns downward, and the graph slopes downward from0to-um/s.
This creates a triangular shape where the peak represents u at t = 0 s, zero at t = 2 s, and -u at t = 4 s.
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 formula for the maximum height reached by a projectile:
h = rac{u^2}{2g}
Where:
his the maximum height (19.6 m)gis the acceleration due to gravity (approximately 9.8 m/s²)
Rearranging this gives:
Substituting the known values:
Calculating this:
Taking the square root:
Thus, the value of u is approximately 19.6 m/s.