Question

a football player kicks a ball at a distance of 10m from vertical pole at an angle of 45 degree the ball just clears the tip of the pole and falls at a distance of 10 m on other side determine the height of the vertical pole

Answer 1

The ball will be in projectile motion.

Range of the projectile,

R=10+10=20m=((u^2)sin2θ)/g......... (1)

Since the ball just clears the tip of the pole, the height of the pole is the maximum height of the projectile.

H=((u^2)*((sinθ)^2))/(2*g)........... (2)

On dividing equation (1) by (2),

20/H=[((u^2)sin2θ)/g]/[((u^2)*((sinθ)^2))/(2*g)]

On further solving, we arrive at this:

20/H=4

Therefore,

H=5m

Thus the pole was of height 5 metres.

Hope it helps ;)

Answer 2

Answer: Based on the given data in question , the height of the vertical pole is approximately 5.10 meters.

Explanation:Let  solve this problem by breaking it down into two parts: the horizontal distance traveled by the ball and the vertical height of the pole.

Horizontal Distance:

The horizontal distance traveled by the ball is 10m on one side and 10m on the other side of the pole, which means the total horizontal distance traveled by the ball is 20m.

Vertical Height:Let's consider the motion of the ball when it is at its highest point. At this point, the vertical velocity of the ball is zero. We can use this fact to calculate the height of the pole.

We know that the initial vertical velocity of the ball is given by:

v₀ = u sin(θ)

where u is the initial velocity of the ball and θ is the angle of projection (45 degrees in this case).

At the highest point, the vertical velocity of the ball is zero, so we can use the following equation to find the time taken by the ball to reach this point:

v = u + at

where v is the final velocity (which is zero), a is the acceleration due to gravity (-9.8 m/s²), and t is the time taken to reach the highest point.

Rearranging this equation, we get:

t = u/a sin(θ)

Now we can use the following equation to find the height of the pole:

h = u²/2a sin²(θ)

Substituting the given values, we get:

h = (u²/2a) * (sin²(θ))

= ((10²)/(2*9.8)) * (sin²(45))

≈ 5.10 m

Therefore, the height of the vertical pole is approximately 5.10 meters.

Learn more about velocity:https://brainly.in/question/11504533

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