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Question: You stand at the bottom of a long ramp (i.e. one used for wheelchair access)...

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You stand at the bottom of a long ramp (i.e. one used for wheelchair access) and throw a tennis ball towards the top of the ramp, as shown in the sketch. Assume that the tennis ball leaves your hands a height h = 1.800 m from the ground and at a speed of v0 = 14.00 m/s and an angle of elevation of 51.03°, as shown in the sketch. Take the origin of a Cartesian coordinate system on the ground, at the point where you are standing, with the x-axis horizontally forwards and the y-axis vertically upwards. Take g = 9.803 m/s2 and choose t= 0 s the instant that the ball is released. Treat the ball as a point mass and ignore the effects of air resistance.

  1. Write the acceleration vector a of the tennis ball in unit vector notation in the given coordinate system.

  2. Write down the initial velocity v(0) of the tennis ball in unit vector notation in the given coordinate system.

  3. Calculate the velocity of the tennis ball as a function of the time v(t).

  4. Calculate the position of the tennis ball r(t) as a function of the time.

  5. Eliminate t from your answer for r(t) and determine the equation of path (trajectory) of the tennis ball in Cartesian form: y = y(x)

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