Question

practice

1. a skateboarder slides 4.2 m up a ramp, stops, and then slides 2.7 m down the ramp before jumping off.

(a) sketch a diagram of the motion showing the displacement vectors and the total displacement vector.
(b) what is his total displacement up the ramp?
(c) what is his total distance?
(b) \\( \delta d _ { t } = 1.5 \mathrm { m } \mathrm { up } \\)
(c) \\( d _ { t } = 6.9 \mathrm { m } \\)

Explanation:

Step1: Determine displacement

Displacement is a vector quantity. Let the upward direction be positive. The first displacement \(d_1 = 4.2\ m\) (up), the second displacement \(d_2=- 2.7\ m\) (down). The total displacement \(\Delta d_T=d_1 + d_2\).

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Since the result is positive, the direction is up.

Step2: Determine distance

Distance is a scalar quantity. It is the sum of the magnitudes of each part of the motion. Let \(d_1 = 4.2\ m\) and \(d_2 = 2.7\ m\). The total distance \(d_T=d_1 + d_2\).

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Answer:

(b) The total displacement up the ramp is \(1.5\ m\) [up].
(c) The total distance is \(6.9\ m\).