A ball was tossed at a height of 1.0 m from the floor with an initial velocity of 5.0 m/s and landed in a basket across the room

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Question 1 [40 marks]

A ball was tossed at a height of 1.0 m from the floor with an initial velocity of 5.0 m/s and landed in a basket across the room which has the same height as where the ball was thrown (1.0 m). The horizontal and vertical position of the ball (x, y) during the toss was recorded using motion sensors which has an accuracy of +5 cm. Figure 1 illustrates the projectile motion of the thrown ball. The recorded positions of the ball (x, y) during the toss are also shown on Figure 1.

In your solution, take the acceleration due to gravity as g = 9.81 ms.

a) For the vertical direction (y), assume that the maximum kinetic energy of the ball is equal to TWICE the maximum potential energy of the ball. Hence, determine analytically the maximum height that the ball would achieve during the toss with reference to the floor (y = 0).

b) For the horizontal direction (x), assume that the maximum kinetic energy of the ball is equal to HALF the maximum potential energy of the ball. Hence, determine analytically the total horizontal difference travelled by the ball from x = 0 to the basket.

c) Fit a curve to the data provided in Figure 1 and determine the maximum height of the ball from the floor (y = 0) and the total horizontal distance travelled by the ball using your fitted curve.

d) Using the curve fit from c) determine the initial angle in degrees that the ball was thrown using a second order accurate numerical method with a step size of 0.25 m.

e) Find the percentage error between your answers in c) with a) and b). Based on your answer in d), what can you say about the data in Figure 17

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