Question

A green grasshopper accelerates from rest to a velocity of 90 cm/s in 5 ms. Assuming constant acceleration for its vertical jump from the ground

Answer 1

The boy travels a distance of 1000 m on the merry-go-round.

Step-by-step explanation:

The distance travelled by the boy can be calculated using the formula for angular displacement:

θ = ωi * t + 0.5 * α * t^2

Where:

θ is the angular displacement,

ωi is the initial angular velocity,

t is the time, and

α is the angular acceleration.

In this case, the initial angular velocity (ωi) is 0 rad/s, and the final angular velocity (ωf) is 5 rad/s. The acceleration (α) can be calculated using the formula:

α = (ωf - ωi) / t

Substituting the values into the formula:

α = (5 rad/s - 0 rad/s) / 20 s = 0.25 rad/s^2

Now we can calculate the angular displacement (θ):

θ = (0 rad/s * 20 s) + 0.5 * (0.25 rad/s^2) * (20 s)^2 = 200 rad

The distance travelled by the boy can be calculated using the formula:

d = r * θ

Where:

d is the distance,

r is the radius of the merry-go-round, and

θ is the angular displacement.

Substituting the values into the formula:

d = 5 m * 200 rad = 1000 m