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The ceiling of a hall is 40 m high. For maximum horizontal distance, the angle at which the ball may be thrown with a speed of 56 m/s without hitting the ceiling of the hall is
- a)25o
- b)30o
- c)45o
- d)60o
Correct answer is option 'B'. Can you explain this answer?
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The ceiling of a hall is 40 m high. For maximum horizontal distance, t...
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The ceiling of a hall is 40 m high. For maximum horizontal distance, t...
To determine the maximum horizontal distance the ball can be thrown without hitting the ceiling, we need to analyze the projectile motion of the ball.
When the ball is thrown, it follows a curved trajectory due to the combination of its initial horizontal velocity and vertical acceleration due to gravity.
To find the angle at which the ball can be thrown without hitting the ceiling, we need to consider the maximum height the ball reaches during its trajectory. If this maximum height is less than the height of the ceiling, the ball will not hit the ceiling.
Let's break down the problem step by step:
1. Determine the maximum height of the ball:
The maximum height of the ball can be determined using the equation for vertical motion:
h = (v^2 * sin^2θ)/(2g)
where h is the maximum height, v is the initial velocity of the ball, θ is the angle of projection, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Plugging in the given values:
h = (56^2 * sin^2θ)/(2*9.8)
h = (3136 * sin^2θ)/19.6
h = 160 * sin^2θ
2. Compare the maximum height with the height of the ceiling:
Since the height of the ceiling is given as 40 m, we can set up the following inequality:
160 * sin^2θ < />
sin^2θ < />
sin^2θ < />
3. Solve for the angle θ:
Taking the square root of both sides of the inequality, we get:
sinθ < />
To find the maximum angle, we need to determine the angle whose sine is less than 0.5. By referring to the trigonometric table or using a calculator, we find that sin^-1(0.5) is equal to 30 degrees.
Therefore, the maximum angle at which the ball can be thrown without hitting the ceiling is 30 degrees. Hence, the correct answer is option B.
When the ball is thrown, it follows a curved trajectory due to the combination of its initial horizontal velocity and vertical acceleration due to gravity.
To find the angle at which the ball can be thrown without hitting the ceiling, we need to consider the maximum height the ball reaches during its trajectory. If this maximum height is less than the height of the ceiling, the ball will not hit the ceiling.
Let's break down the problem step by step:
1. Determine the maximum height of the ball:
The maximum height of the ball can be determined using the equation for vertical motion:
h = (v^2 * sin^2θ)/(2g)
where h is the maximum height, v is the initial velocity of the ball, θ is the angle of projection, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Plugging in the given values:
h = (56^2 * sin^2θ)/(2*9.8)
h = (3136 * sin^2θ)/19.6
h = 160 * sin^2θ
2. Compare the maximum height with the height of the ceiling:
Since the height of the ceiling is given as 40 m, we can set up the following inequality:
160 * sin^2θ < />
sin^2θ < />
sin^2θ < />
3. Solve for the angle θ:
Taking the square root of both sides of the inequality, we get:
sinθ < />
To find the maximum angle, we need to determine the angle whose sine is less than 0.5. By referring to the trigonometric table or using a calculator, we find that sin^-1(0.5) is equal to 30 degrees.
Therefore, the maximum angle at which the ball can be thrown without hitting the ceiling is 30 degrees. Hence, the correct answer is option B.
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The ceiling of a hall is 40 m high. For maximum horizontal distance, t...
In this question from projectile motion. we know, maximum height is 40m. gravity g can be taken as 10 m/s^2. we also know that initial velocity is 56m/s. we have to find angle of projection. on applying the formula, H = (u^2 sin^2 ø)/2g, will get 30 degrees as the answer.
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The ceiling of a hall is 40 m high. For maximum horizontal distance, the angle at which the ball may be thrown with a speed of 56 m/s without hitting the ceiling of the hall is a)25ob)30oc)45od)60oCorrect answer is option 'B'. Can you explain this answer?
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