Q29 of 32 Page 85

A bullet fired at an angle of 30° with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0 km away? Assume the muzzle speed to be fixed, and neglect air resistance.

Now this is the case of projectile motion, the motion of bullet will be a projectile and its path will be parabola, the motion of bullet can be divided into horizontal component and vertical component i.e. motion along x axis and motion along y axis


Now the bullet is only experiencing one force in vertically downward direction because of its weight (gravitational force of earth) due to which its accelerating along negative y axis due to acceleration due to gravity, acceleration is uniform i.e. all the three equations of motion are valid in along Y direction, now there is no force in horizontal direction so component of velocity in horizontal direction or along X axis would remain constant.


The projectile motion of bullet has been shown in the figure



Now for an particle projected at an angle

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27

A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector? The rotation of a body can be specified by the direction of the axis of rotation, and the angle of rotation about the axis. Does that make any rotation a vector?

 28

Can you associate vectors with (a) the length of a wire bent into a loop, (b) a plane area, (c) a sphere? Explain.

 30

A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 ms-1 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m s-2).

 31

A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?