A cricket player bowls a 100g cricket ball, releasing it from a height of exactly 1.1m. Ignoring the effect of air resistance, if the cricket player wants to release the ball such that its velocity is exactly parallel to the ground, at what velocity does she need to release it so that it will land 13.8m from the point of release?Note: The height the ball has been released may have changed.Give your answer to one decimal place in units of m/s. Do not include the units in your answer i.e. you would write 8.6 m/s as 8.6
Question
A cricket player bowls a 100g cricket ball, releasing it from a height of exactly 1.1m. Ignoring the effect of air resistance, if the cricket player wants to release the ball such that its velocity is exactly parallel to the ground, at what velocity does she need to release it so that it will land 13.8m from the point of release?Note: The height the ball has been released may have changed.Give your answer to one decimal place in units of m/s. Do not include the units in your answer i.e. you would write 8.6 m/s as 8.6
Solution
To solve this problem, we need to use the equations of motion.
First, we need to find the time it takes for the ball to hit the ground after being released. We can use the equation of motion:
h = 0.5 * g * t^2
where h is the height from which the ball is released (1.1m), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time we want to find.
Rearranging the equation to solve for t gives us:
t = sqrt((2 * h) / g)
Substituting the given values gives us:
t = sqrt((2 * 1.1) / 9.8) = 0.475 seconds
Next, we need to find the velocity at which the ball needs to be released. We can use the equation:
d = v * t
where d is the distance the ball needs to travel (13.8m), v is the velocity we want to find, and t is the time we found earlier.
Rearranging the equation to solve for v gives us:
v = d / t
Substituting the given values gives us:
v = 13.8 / 0.475 = 29.1 m/s
So, the cricket player needs to release the ball at a velocity of 29.1 m/s.
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