A monkey can jump a maximum horizontal distance of 40 m. Then the velocity of the monkey is (g = 10 m/s²)?

Question

Answer

Explanation:

Given, the maximum horizontal distance the monkey can jump is 40 m.

Let us assume that the monkey jumps at an angle of 45 degrees with respect to the horizontal.

The time taken by the monkey to reach the maximum height can be calculated as:

u = initial velocity of the monkey = 0 (as the monkey starts from rest)

v = final velocity of the monkey at maximum height = 0 (as the monkey reaches maximum height and starts falling down)

a = acceleration due to gravity = -10 m/s² (as the monkey is moving upwards against the gravitational force)

s = maximum height reached by the monkey = H

Using the equation of motion:

H = ut + (1/2)at²

H = 0 + (1/2)(-10)t²

H = -5t²

Similarly, the time taken by the monkey to reach the maximum horizontal distance can be calculated as:

u = initial velocity of the monkey = 0 (as the monkey starts from rest)

v = final velocity of the monkey at maximum distance = ?

a = acceleration due to gravity = -10 m/s² (as the monkey is moving horizontally against the gravitational force)

s = maximum horizontal distance reached by the monkey = 40 m

Using the equation of motion:

s = ut + (1/2)at²

40 = 0t + (1/2)(-10)t²

t = 4 seconds

Now, using the time taken to reach the maximum height, we can calculate the initial vertical velocity of the monkey as:

u = initial velocity of the monkey = ?

a = acceleration due to gravity = -10 m/s² (as the monkey is moving upwards against the gravitational force)

t = time taken to reach maximum height = 2 seconds (as the monkey takes equal time to reach maximum height and come down)

v = final velocity of the monkey at maximum height = 0 (as the monkey reaches maximum height and starts falling down)

Using the equation of motion:

v = u + at

0 = u + (-10)(2)

u = 20 m/s

Now, using the initial vertical velocity of the monkey, we can calculate the horizontal velocity of the monkey as:

v = horizontal velocity of the monkey = ?

θ = angle of projection = 45 degrees

u = initial vertical velocity of the monkey = 20 m/s

Using the equation of motion:

v = u*cos(θ)

v = 20*cos(45)

v =

Answer

R = u^2 sin2

θ/ g

R max = u^2/g

40= u^2/g

u^2/10 = 40
u^2 = 400

u = 20 m /s

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