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  • A man runs across the roof-top of a tall building and jumps horizontally with the hope of landing on the roof of the next building which is of a lower height than the first.

A man runs across the rooftop of a tall building and jumps horizontally with the hope of landing on the roof of the next building which is of a lower height than the first. If his speed is 9 m/s, the horizontal distance between the two buildings is 10 m and the height difference is 9 m, will he be able to land on the next building?

Answers (1)

Given, the horizontal speed of the man is, u_{x} = 9 m/s

The horizontal distance between the two buildings is, x = 10 m

The height difference between the two buildings is, h = 9 m

The initial vertical speed of the man is, u = 0

The acceleration due to gravity is, a = 10 m/s^2

The vertical displacement is given as, h = u t + 1/2 a t^2

Substitute the values to get, 9 = 0 + 1/2 (10) t^2

Simplifying, 9 = 5 t^2

Solving for time, t = sqrt(9/5)

This gives, t = sqrt(9)/sqrt(5)

Now, the horizontal distance travelled by the man is, u_x * t = 9 * sqrt(9/5)

Simplifying, = 27/sqrt(5)

Now, multiplying by sqrt(5)/sqrt(5), we get, = 27 * sqrt(5)/5

Calculating, = 12.07 m

Hence, the person will land on the next building, which is farther by, 12.07 - 10 = 2.07 m.

As the horizontal distance travelled by the man is greater than the distance between the two buildings i.e.10 m. so, YES, the man will land on the next building

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