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 cms, 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?

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 velocitymathematically p = mΔvp = momentum, m = mass of the body, Δv = change in velocityacceleration a = Δv/ΔtΔv = aΔt

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

mathematically I = FΔt

as such Impulse = change in momentumI = ΔpmΔv = I = FΔtΔt = mΔv/Fbut m = 1.0 x 10^10 kg, Δv = 0.20cm/s or 0.002m/s, F = 2.5NPlugging the values into ; Δt = mΔv/F = 1.0 x 10^10 kg x 0.002m/s x 2.5NΔt = 8 x 10^6secs , Δt in days = 92.6daysN/B ; 1 day = 86400secs