Question

A ""doomsday"" asteroid with a mass of 1.0 * 1010 kg is hurtling through space. Unless the asteroid’s speed is changed by about 0.20 cm????s, it will collide with Earth and cause tremendous damage. Researchers suggest that a small ""space tug"" sent to the asteroid’s surface could exert a gentle constant force of 2.5 N. For how long must this force act?

Answer 1

Answer:

Δt = 8 x 10^6secs , Δt in days = 92.6days

1 day = 86400secs

Explanation:

• The concept of momentum is applied here.

• momentum is the product of mass and change in velocity

• mathematically p = mΔv

• p = momentum, m = mass of the body, Δv = change in velocity

• acceleration a = Δv/Δt

• Δv = aΔt

the impulse is the product of the force and the change in time;

mathematically I = FΔt

• as such Impulse = change in momentum

• I = Δp

• mΔv = I = FΔt

• Δt = mΔv/F

• but m = 1.0 x 10^10 kg, Δv = 0.20cm/s or 0.002m/s, F = 2.5N

• Plugging the values into ; Δt = mΔv/F = 1.0 x 10^10 kg x 0.002m/s x 2.5N

• Δt = 8 x 10^6secs , Δt in days = 92.6days

• N/B ; 1 day = 86400secs