Problems class 4. Motion in 2 dimensions 1) A particle is projected horizontally

Question

Problems class 4. Motion in 2 dimensions 1) A particle is projected horizontally at 36 m/s from a point 122.5 m above a distance travelled in that time. horizontal surface. Find the tme taken by the particle to reach the surface and the horizontal 2) A particle is projected horizontally with a speed of 14.7 m/s. Find the horizontal and vertical displacements of the particle from the point of projection after 2 seconds. Find also how far the particle is from the point of projection. 3) A particle is projected horizontally from a point 44.1 m above a horizontal plane. The particle hits the ground at a point which is 39 m from the point of the projection. Find the initial speed of the particle. 4) A particle is projected horizontally with a velocity of 39.2 m/s. Find the horizontal and vertical components of the velocity of the particle 3 seconds after projection. Also find the speed and direction of motion of the particle at this time. 5) A particle is projected from a point on a horizontal plane and has an initial velocity of 2813 m/s at an angle of elevation of 60 deg. Find the greatest height reached by the particle and the time taken to reach this point. 6) A particle is projected from a point on a horizontal plane and has an initial velocity of 45 m/s at an angle of elevation of tan 3/4. Find the time of flight and the range of the particle on the horizontal plane. 7) a small ball suspended from a string is set into oscillator motion, when the ball passes through its lowest point the string is cut. If the ball is then moving with a velocity of 0.8 m/s at a height of 5 m above the ground find the horizontal distance travelled by the ball Assume g = 10 ms speed in SI units does the puma leave the ground at? height. What is the angle of projection? 8) pumas can leap up to 12 ft high when leaving the ground at an angle of 45°. What is the 9) a projectile is fired in such a way that its horizontal range is three times its maximum 10) a firefighter a distance d from a burning building directs a stream of water from a hose at an angle ' above the horizontal. If the initial speed is v, at what height does the water strike the building? 11) a placekicker must kick a rugby ball from a point 36m in front of the goal above the crossbar which is 3.05m high. When kicked the ball leaves the ground with a speed of 20m/s at an angle of 53° to the horizontal. Does the ball clear the bar and if so by how much /or how much does the ball fall short of clearing the bar? Does the ball approach the cross bar whilst still rising or falling?

Explanation / Answer

(1) ans

Given that

Initial velocity u=36 m/s

Height h=122.5 m

Now we find the time taken to reach the ground

Time t=(2*122.5/9.8)^1/2=5s

Now we find the horizontal range

Range R=36*5=180 m

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(2) ans

Given that

Initial velocity u=14.7 m/s

Now we find the horizontal and vertical displacement

Horizontal displacement =ut=14.7*2=29.4 m

Vertical displacement =1/2*9.8*2^2=19.6 m

(3) ans

Given that

Horizontal displacement R=44.1 m

Vertical displacement h=39 m

Now we find the initial velocity

R=u(2h/g)^1/2

44.1=u*(2*39/9.8)^1/2

Initial velocity u=15.6m/s

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