The ceiling of a long hall is 25m high. What is the maximum horizontal distance that a ball thrown with a speed of 40m/s can go without hitting the ceiling of the hall?

Question

Answer

See Sharon it's all about formulas

now see
given
max height =25
and angle is given by
theta (0) Sharon u please assume 0 as theta
now
h=u2sin20/2*9.8. (gravity
sin20=0.30625
sin0=0.5534

therefore,
0=sin(0.5534)=33.60
we know
horizontal range
R=u2sin20/g
so
abhi values bitha do
=(40)2*sin(2*33.60)/9.8

rest can you please do friend

Answer

Given,
Hight of Hall( H) = 25 m
Let ball is thrown with speed 40m/s at an angle ∅ with horizontal .

We know,
H = u²sin²∅/2g
25= (40)² × sin²∅/2× 10
25 = 80 × sin²∅
Sin²∅ = 25/80
Sin∅ = 5/4√5
Cos∅ = √55/4√5

Now, horizontal range = u²sin2∅/g
= (40)²× 2sin∅×cos∅/g
= 160 × 2 × 5/4√5 × √55/4√5
= 20√55 m

Hope it helps you
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Answer

The Problem

The problem states that the ceiling of a long hall is 25m high, and we need to determine the maximum horizontal distance that a ball thrown with a speed of 40m/s can travel without hitting the ceiling.

Understanding the Situation

To solve this problem, we need to consider the motion of the ball in two dimensions: horizontal and vertical. The ball follows a parabolic trajectory due to the force of gravity acting on it. The horizontal motion is uniform, while the vertical motion is affected by gravity.

Breaking Down the Solution

To find the maximum horizontal distance, we can use the following steps:

1. Determine the time of flight: Since the ball follows a parabolic trajectory, the time taken to reach the highest point will be equal to the time taken to reach the same height on the way down. The total time of flight can be calculated using the formula:
t = (2 * v₀ * sin(θ)) / g
where v₀ is the initial velocity (40m/s), θ is the angle of projection, and g is the acceleration due to gravity (9.8m/s²).

2. Calculate the maximum height reached by the ball: Using the time of flight, we can determine the maximum height by substituting the value into the equation:
h = (v₀² * sin²(θ)) / (2 * g)

3. Check if the maximum height is less than the ceiling height: If the maximum height is less than 25m, the ball will not hit the ceiling. Otherwise, we need to calculate the horizontal distance.

4. Calculate the horizontal distance: The horizontal distance can be calculated using the formula:
d = v₀ * cos(θ) * t
where v₀ is the initial velocity (40m/s), θ is the angle of projection, and t is the time of flight.

5. Round the answer: Finally, round the horizontal distance to the nearest whole number to obtain the maximum horizontal distance that the ball can travel without hitting the ceiling.

Conclusion

By following these steps, we can determine the maximum horizontal distance that a ball thrown with a speed of 40m/s can travel without hitting the ceiling of the hall.

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