Question

A toy car runs off the edge of a table that
is 1.267 m high. The car lands 0.5736 m from
the base of the table.
How long does it take for the car to fall?
The acceleration due to gravity is 9.8 m/s
What is the horizontal velocity of the car?

Answer 1

1. A toy car runs of the edge of a table that is $1.267\,\mathrm{m}$ high. The car lands $0.5736\,\mathrm{m}$ from the base of the table. How long does it take for the car to fall? The acceleration due to gravity is $9.8\,\mathrm{m/s}$. What is the horizontal velocity of the car?

According to the condition of the problem, at the moment of the landing,

$$d = v_0 t, \quad h = \frac{g t^2}{2}.$$

So, the time of the flight is

$$t = \sqrt{\frac{2h}{g}}.$$

The initial velocity is

$$v_0 = \frac{d}{t}.$$

Let check the dimensions.

$$[t] = \sqrt{\frac{\mathrm{m}}{\mathrm{m}} \cdot \frac{\mathrm{m}}{\mathrm{s}^2}} = s, \quad [v_0] = \frac{\mathrm{m}}{\mathrm{s}}.$$

Let evaluate the quantities.

$$t = \sqrt{\frac{2 \cdot 1.267}{9.8}} = 0.5085\,(\mathrm{s}), \quad v_0 = \frac{0.5736}{0.5085} = 1.128\left(\frac{\mathrm{m}}{\mathrm{s}}\right).$$

Answer: $0.5085\,s$, $1.128\,\frac{\mathrm{m}}{\mathrm{s}}$.