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A cricketer can throw a ball to a maximum horizontal distance of 100m. With the same speed how much high above the ground can the cricketer throw the same ball?
- a)50 m
- b)100 m
- c)150 m
- d)200 m
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A cricketer can throw a ball to a maximum horizontal distance of 100m....
Let u be the velocity of projection of the ball. The ball will cover maximum horizontal distance when angle of projection with horizontal, θ = 45∘. Then Rmax = u2/g = 100m
If ball is projected vertically upwards (θ = 90∘) from ground then H attains maximum value.
∴ The height to which cricketer can through the ball is = Rmax/2 = 100/2 = 50m.
If ball is projected vertically upwards (θ = 90∘) from ground then H attains maximum value.
∴ The height to which cricketer can through the ball is = Rmax/2 = 100/2 = 50m.
Most Upvoted Answer
A cricketer can throw a ball to a maximum horizontal distance of 100m....
To understand this problem, we need to consider the motion of the ball thrown by the cricketer. The ball follows a projectile motion, which can be broken down into horizontal and vertical components.
Horizontal Motion:
The maximum horizontal distance that the ball can travel is 100m. This means that the ball will cover this distance in the horizontal direction before hitting the ground. The horizontal motion of the ball is not affected by gravity, as there is no force acting on it in the horizontal direction. Therefore, the speed of the ball in the horizontal direction remains constant throughout its motion.
Vertical Motion:
The vertical motion of the ball is affected by the force of gravity. When the ball is thrown, it goes up, reaches a maximum height, and then falls back down. The time it takes for the ball to reach its maximum height is the same as the time it takes for the ball to fall back down to the ground. This is because the vertical motion is symmetric.
Since we know that the maximum horizontal distance is 100m, we can use this information to find the time of flight of the ball. The time of flight is the total time it takes for the ball to complete its motion from being thrown to hitting the ground. We can use the formula for horizontal distance and time of flight:
Horizontal distance = (initial horizontal velocity) * (time of flight)
In this case, the horizontal distance is 100m, and the initial horizontal velocity is the same as the speed at which the ball is thrown. Therefore, we can rewrite the formula as:
100m = (initial horizontal velocity) * (time of flight)
Since we are given that the maximum horizontal distance is 100m, we can conclude that the time of flight is the same for both the horizontal and vertical motion.
Now, let's consider the vertical motion of the ball. Since the time of flight is the same for both the horizontal and vertical motion, we can use the formula for vertical distance:
Vertical distance = (initial vertical velocity) * (time of flight) - (0.5) * (acceleration due to gravity) * (time of flight)^2
In this case, the vertical distance is the maximum height that the ball can reach. We want to find this height. The initial vertical velocity is the speed at which the ball is thrown vertically upwards. The acceleration due to gravity is a constant value of 9.8 m/s^2. Therefore, we can rewrite the formula as:
Maximum height = (initial vertical velocity) * (time of flight) - (0.5) * (acceleration due to gravity) * (time of flight)^2
Since the time of flight is the same for both the horizontal and vertical motion, we can substitute this value into the formula:
Maximum height = (initial vertical velocity) * (time of flight) - (0.5) * (acceleration due to gravity) * (time of flight)^2
= (initial vertical velocity) * (time of flight) - (0.5) * (acceleration due to gravity) * (time of flight)^2
= (initial vertical velocity) * (time of flight) - (0.5) * (9.8 m/s^2) * (time of flight)^2
Since the time of flight is the same for both the horizontal and vertical motion, we can conclude that the maximum height is determined by the initial vertical velocity. Therefore
Horizontal Motion:
The maximum horizontal distance that the ball can travel is 100m. This means that the ball will cover this distance in the horizontal direction before hitting the ground. The horizontal motion of the ball is not affected by gravity, as there is no force acting on it in the horizontal direction. Therefore, the speed of the ball in the horizontal direction remains constant throughout its motion.
Vertical Motion:
The vertical motion of the ball is affected by the force of gravity. When the ball is thrown, it goes up, reaches a maximum height, and then falls back down. The time it takes for the ball to reach its maximum height is the same as the time it takes for the ball to fall back down to the ground. This is because the vertical motion is symmetric.
Since we know that the maximum horizontal distance is 100m, we can use this information to find the time of flight of the ball. The time of flight is the total time it takes for the ball to complete its motion from being thrown to hitting the ground. We can use the formula for horizontal distance and time of flight:
Horizontal distance = (initial horizontal velocity) * (time of flight)
In this case, the horizontal distance is 100m, and the initial horizontal velocity is the same as the speed at which the ball is thrown. Therefore, we can rewrite the formula as:
100m = (initial horizontal velocity) * (time of flight)
Since we are given that the maximum horizontal distance is 100m, we can conclude that the time of flight is the same for both the horizontal and vertical motion.
Now, let's consider the vertical motion of the ball. Since the time of flight is the same for both the horizontal and vertical motion, we can use the formula for vertical distance:
Vertical distance = (initial vertical velocity) * (time of flight) - (0.5) * (acceleration due to gravity) * (time of flight)^2
In this case, the vertical distance is the maximum height that the ball can reach. We want to find this height. The initial vertical velocity is the speed at which the ball is thrown vertically upwards. The acceleration due to gravity is a constant value of 9.8 m/s^2. Therefore, we can rewrite the formula as:
Maximum height = (initial vertical velocity) * (time of flight) - (0.5) * (acceleration due to gravity) * (time of flight)^2
Since the time of flight is the same for both the horizontal and vertical motion, we can substitute this value into the formula:
Maximum height = (initial vertical velocity) * (time of flight) - (0.5) * (acceleration due to gravity) * (time of flight)^2
= (initial vertical velocity) * (time of flight) - (0.5) * (acceleration due to gravity) * (time of flight)^2
= (initial vertical velocity) * (time of flight) - (0.5) * (9.8 m/s^2) * (time of flight)^2
Since the time of flight is the same for both the horizontal and vertical motion, we can conclude that the maximum height is determined by the initial vertical velocity. Therefore
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A cricketer can throw a ball to a maximum horizontal distance of 100m. With the same speed how much high above the ground can the cricketer throw the same ball?a)50 mb)100 mc)150 md)200 mCorrect answer is option 'A'. Can you explain this answer?
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