Question

A horizontally thrown dart falls 5 cm before it travels 2. 5 m to hit the dart board. how fast was it thrown?

Answer 1

The dart player throws a dart horizontally at a speed of 24.75 m/s.

In this question,

The horizontal distance traveled by the dart, x = 2.5 m

The dart hits the board 5 cm below the height from which it was thrown.

⇒ 5 cm = 0.05 m

Let the time taken by the dart to hit the board is t.

The time taken can be calculated using the Newton's second law of motion,

$y = ut+\frac{1}{2}at^{2}$

Put, u = 0, a = -g and g = 9.8

On substituting the above values, we get

⇒ $-0.05 = 0-\frac{1}{2}(9.8)t^{2}$

⇒ $0.05(\frac{2}{9.8}) = t^{2}$

⇒ $t^{2} =0.0102$

⇒ $t=\sqrt{0.0102}$

⇒ t = 0.1010 s

Now, the velocity (speed) can be calculated as

displacement = speed × time

⇒ 2.5 = speed × 0.1010

⇒ speed = $\frac{2.5}{0.1010}$

⇒ speed = 24.7524 m/s

Hence we can conclude that the dart player throws a dart horizontally at a speed of 24.75 m/s.

Learn more about dart and Newton's second law of motion here

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