An Olympic diver is on a diving platform 3.80 m above the water. To start her dive, she runs off of the platform with a speed of
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This question involves the concepts of the law of conservation of momentum and velocity.
The velocity of the eight ball is "5.7 m/s".
According to the law of conservation of momentum:
where,
m₁ = mass of number three ball = 5 g
m₂ = mass of the eight ball = 6 g
u₁ = velocity of the number three ball = 3 m/s
u₂ = velocity of the eight ball = - 1 m/s (negative sign due to opposite direction)
v₁ = final velocity of the three number ball = - 5 m/s
v₂ = final velocity of the eight ball = ?
Therefore,
(5 g)(3 m/s) + (6 g)(- 1 m/s) = (5 g)(- 5 m/s) + (6 g)(v₂)
<u>v₂ = 5.7 m/s</u>
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Learn more about the law of conservation of momentum here:
(a) The launching velocity of the beetle is 6.4 m/s
(b) The time taken to achieve the speed for launch is 1.63 ms
(c) The beetle reaches a height of 2.1 m.
(a) The beetle starts from rest and accelerates with an upward acceleration of 400 g and reaches its launching speed in a distance 0.53 cm. Here g is the acceleration due to gravity.
Use the equation of motion,
Here, the initial velocity of the beetle is u, its final velocity is v, the acceleration of the beetle is a, and the beetle accelerates over a distance s.
Substitute 0 m/s for u, 400 g for a, 9.8 m/s² for g and 0.52×10⁻²m for s.
The launching speed of the beetle is <u>6.4 m/s</u>.
(b) To determine the time t taken by the beetle for launching itself upwards is determined by using the equation of motion,
Substitute 0 m/s for u, 400 g for a, 9.8 m/s² for g and 6.385 m/s for v.
The time taken by the beetle to launch itself upwards is <u>1.62 ms</u>.
(c) After the beetle launches itself upwards, it is acted upon by the earth's gravitational force, which pulls it downwards towards the earth with an acceleration equal to the acceleration due to gravity g. Its velocity reduces and when it reaches the maximum height in its path upwards, its final velocity becomes equal to zero.
Use the equation of motion,
Substitute 6.385 m/s for u, -9.8 m/s² for g and 0 m/s for v.
The beetle can jump to a height of <u>2.1 m</u>