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 14.14 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. What is the distance of the car from the gun when the shell hits it?

250 m

Explanation:

In projectile, range is given as;

R = (v²sin 2θ)/g

We are given θ = 45°

Thus range of shell is;

R = (v²sin (2 × 45))/g

R = v²/g

Now, distance for the shell to hit the car will be; 150 + 14.14t

This will be equal to the range of shell;

150 + 14.14t = v²/g

Where t is time of flight

Now, time of flight is given by;

t = (2vsin θ)/g

t = (2v sin 45)/g

In surf form, we have;

t = (2v/(g√2))

Simplifying further gives;

t = (v√2)/g

Plugging this value of t into the distance equation gives;

150 + 14.14(v√2)/g = v²/g

Assuming g is 10 m/s², we have;

150 + 14.14(v√2)/10 = v²/10

Multiply through by 10 to get;

1500 + 14.14(v√2) = v²

v² - 20v - 1500 = 0

From quadratic equation calculator, we have; v = 50 m/s

Thus, t = (50√2)/g

t = (50√2)/10

t = 5√2

Plugging this into the distance equation gives;

Distance = 150 + 14.14(5√2) = 250 m

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.