Once upon a time, a famous zoologist was hunting antelope for a zoo with a dart

Question

Once upon a time, a famous zoologist was hunting antelope for a zoo with a dart gun that fired darts with a range of 100 m at a speed of 25 m/s. If he shot a dart at an antelope at rest 50 m away, and the antelope instantly began to accelerate at a constant rate away from the dart, running out of range of the dart just in time:

a) Find the minimum acceleration of the antelope
b) Find the maximum time the antelope can remain in range of the dart; (10 points)
c) Find the minimum speed of the antelope as it runs out of range of the dart. (6 points)

Explanation / Answer

the speed of the dart V = 25 m/s , distance d = 100 m (a) the time taken to the dart to reach the range t = 100/25 = 4 s at this time the antelope reach the range , therefore According to equations of motion, S = ut + 1/2at^2 ------------ (1) 50 = 1/2*a*16 a = 6.25 m/s^2 the minimum acceleration of the antelope is 6.25 m/s^2. (b) From equation (1), S = 1/2*a*t^2 t ^2 = 100/6.25 t = 4 S the maximum time the antelope can remain in range of the dart. (c) the speed of the antelope,    From equation of motion V = at    V = 6.25*4 = 25 m/s the minimum speed of the antelope as it runs out of range of the dart is 25 m/s.

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