Determine the following for the block. (Indicate the direction with the sign of your answer.)

Question

A block is fired up an incline and a record of its position as a function of time is shown in the graph. The y-coordinate in the graph represents the distance along the incline, measured from the base of the incline.

Coordinates for the data points are as shown in the table below.

cords : (0,2.00),(1.00,5.00),(2.00,6.00),(3.00,5.00),(4.00,2.00)

A tangent line has been drawn at t = 1.00 s, and this line also passes through the point (2.00 s, 7.00 m). A second tangent line has been drawn at t = 4.00 s, and this line also passes through the point (4.50 s, 0 m).

Determine the following for the block. (Indicate the direction with the sign of your answer.)

a)  the average velocity as it travels from the launch position to the maximum height = ? m/s

b) the instantaneous velocity at a time equal to half the time to go from the launch position to the maximum height = ? m/s

c) the instantaneous velocity at the top of the trajectory = ? m/s

d) the instantaneous velocity when it is back down to the launch position = ? m/s

e)  the launch velocity = ? m/s

Answer 1

It looks like the maximum height is at t=2. This is an assumption based on the height being 5 at t=1 and t=3, and assuming that there are no weird complexities between these times.

The average velocity at the maximum height is given by

v = ∆s / ∆t

where ∆t = 2 and ∆s is the distance between the heights at t=2 and t=0.

Instantaneous velocity is given by the slope of the tangent line, which is given for questions b-d.

If you ignore friction, the launch velocity and the final velocity should be the same, since height is the same at the start and the end.