Question

Greta is on the chairlift going up the mountain when one of her skis falls off.

The ski has a mass of 5 kg and hits the snow below with a speed of 72 km/h.
How high is the chairlift above the snow when the ski falls off?
(Ignore air resistance.)

Give your answer to the nearest 0.1 m.

Use g = 9.8 m/s2 for the acceleration due to gravity.

Answer 1

`20.4\:\text{m}`

Step-by-step explanation:

We can use the following kinematics equation to find the height of the chairlift above the snow:

`v_f^2=v_i^2+2a\Delta y`.

First, let's convert 72 km/h to m/s:

`72\: \text{km/h}=20\:\text{m/s}`

Since the ski starts with an initial vertical velocity of zero, we have
`v_i=0`. We can now substitute
`v_f=20,v_i=0, a=9.8` and solve for how high the chairlift is above the snow:

`20^2=0^2+2\cdot9.8\cdot \Delta y,\\400=19.6\cdot \Delta y,\\\Delta y =(400)/(19.6)=\boxed{20.4\:\text{m}}`.