Question

A gun kept on a straight horizontal road is used to hit a car travelling on the same road away from the gun at a uniform speed of 14.41 ms -1. The car is at a distance of 150 m from the gun when it is fired at an angle of 45° to the horizontal. With what speed should the shell be projected so that it hits the car? Take g = 10 ms -2.

Answer 1

Answer:

50m/s

Step-by-step explanation:

Assume there is no air resistance.

Range of the projectile (bullet) is given by.

R = u^2sin2ø /g. (ø = 45°, sin90 = 1)

R = u^2/g

Time of flight of the bullet is given by.

T = 2usinø/g

T = 2usin45 /g

T = u√2 /g

Given velocity of car = 14.41 m/s

Distance car would have travelled in t = T sec

s1 = vT = 14.41(u)(1.414)/10

s1 = 2.037u

Distance of car from the gun after T sec.

s = 150 + s1

s = 150 + 2.037u

To hit the car, Range = s

u^2/10 = 150 + 2u. (approx)

u^2 = 1500 + 20u

u^2 - 20u - 1500 = 0

(u-50)(u+30) = 0

u = 50m/s , u = -30m/s

Speed that shall be projected so that the bullet hits the car = 50m/s