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In this lesson, we will learn how to use parametric equation properties to describe a projectileβs motion in x- and y-directions as a function of time.

Q1:

A particle projected with a velocity m/s from a fixed point in a horizontal plane landed at a point in the same plane 360 m away. Find the value of and the projectileβs pathβs greatest height . Take .

Q2:

A particle of mass 0.7 kg is attached to end π΄ of a light rod π΄ π΅ of length 0.7 m. The rod is free to rotate in a vertical plane about π΅ . The particle is held at rest with π΄ π΅ at 4 5 β to the upward vertical. The particle is released. Calculate the tension in the rod as the particle passes through the lowest point of the path, giving your answer to the nearest two decimal places. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

Q3:

A particle projected from the origin π passed horizontally through a point with a position vector of ( 1 0 + 1 0 ) i j m, where i and j are horizontal and vertical unit vectors respectively. Determine the velocity with which the particle left π , considering the acceleration due to gravity to be 9.8 m/s^{2}.

Q4:

A particle started moving from π with a velocity of οΊ 2 β π + 1 5 β π ο m/s, where β π and β π are unit vectors horizontally and vertically upwards respectively. Find, giving your answer to the nearest integer, the distance of the particle from π after 1 s. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

Q5:

A smooth solid hemisphere has its flat surface lying on a horizontal table and its curved surface facing upwards. The flat face of the hemisphere has centre and radius . Point , at which a particle is placed, is the highest point on the hemisphere. is then given an initial horizontal speed , where and the acceleration due to gravity is . Find the angle at which strikes the table to the nearest degree.

Q6:

If a particle was projected from the origin π on a horizontal ground with initial velocity ( 1 7 + 1 1 ) i j m/s, write its position vector at time π‘ seconds. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

Q7:

A particle was projected from a point π with a position vector ( 1 7 + 9 ) i j m relative to the origin π . After 2 seconds, it was at a point ( 3 2 + 5 0 ) i j m relative to π , where i and j are the horizontal and vertical unit vectors respectively. Calculate the distance of the particle from π after a further 5 seconds. Take the acceleration due to gravity to be 9.8 m/s^{2}.

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