All are come togetherball is projected from the ground level in vertically upward direction with an initial velocity u. The ball goes up to a maximum height ( EMG ) and then starts moving downward. Finally the ball falls back on the ground. It is given that motion of the ball under the action of gravity alone( IFYS ) and effect of air resistance, if any, is negligible. What is the value of maximum height up to which the ball goes ? (ONT ) What time does the ball take to reach the highest point during its motion ?
Question
All are come togetherball is projected from the ground level in vertically upward direction with an initial velocity u. The ball goes up to a maximum height ( EMG ) and then starts moving downward. Finally the ball falls back on the ground. It is given that motion of the ball under the action of gravity alone( IFYS ) and effect of air resistance, if any, is negligible. What is the value of maximum height up to which the ball goes ? (ONT ) What time does the ball take to reach the highest point during its motion ?
Solution
The maximum height (H) that the ball reaches can be calculated using the following formula derived from the equations of motion:
H = u² / (2g)
where:
- u is the initial velocity of the ball,
- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).
The time (t) it takes for the ball to reach the highest point can be calculated using the following formula:
t = u / g
where:
- u is the initial velocity of the ball,
- g is the acceleration due to gravity.
These formulas assume that the only force acting on the ball is gravity (i.e., air resistance is negligible).
Similar Questions
Every word problem, there should be a conclusion. therefore add a conclusion to the following answer. "(a) The velocity of the ball at its highest point is 0 m/s. This is because at the highest point, the ball stops moving upwards and is about to start falling downwards. (b) The velocity of the ball 1 second before it reaches its highest point depends on the initial speed and the acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s². So, if we denote the initial speed as v0, then the velocity 1 second before the highest point is v0 - 9.8 m/s. (c) The change in velocity during this 1-second interval is the final velocity minus the initial velocity, which is (v0 - 9.8 m/s) - v0 = -9.8 m/s. (d) The velocity of the ball 1 second after it reaches its highest point is -9.8 m/s. This is because the ball has started to fall and is accelerating downwards due to gravity. (e) The change in velocity during this 1-second interval is the final velocity minus the initial velocity, which is -9.8 m/s - 0 = -9.8 m/s. (f) The change in velocity during the 2-second interval is the final velocity after 2 seconds minus the initial velocity, which is (-9.8 m/s) - (v0 - 9.8 m/s) = -19.6 m/s. (g) The acceleration of the ball during any of these time intervals and at the moment the ball has zero velocity is -9.8 m/s². This is the acceleration due to gravity, and it is always acting on the ball, regardless of its velocity."
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