Motion in a Plane quiz

Which of these is a vector?

The resultant of two equal vectors acting in opposite directions is:

At the highest point of a projectile's path, its velocity is:

The path of a projectile under gravity is a:

In uniform circular motion:

The magnitude of a unit vector is:

The centripetal acceleration in uniform circular motion is directed:

If the speed of a body in a circle of fixed radius doubles, its centripetal acceleration becomes:

The acceleration of a projectile at its highest point is:

The angle between velocity and acceleration in uniform circular motion is:

Define a position vector and a displacement vector. (2 marks)

What is a null vector? Give an example. (2 marks)

State the parallelogram law of vector addition. (2 marks)

If A = 2i + 3j and B = i - 2j, find A + B and A - B. (2 marks)

Why is a projectile's horizontal velocity constant? (2 marks)

A cricketer can throw a ball to a maximum horizontal distance of 80 m. Find the speed of the throw, taking g = 9.8 m/s^2. (2 marks)

Write the equations of motion in vector form for constant acceleration. (2 marks)

What is angular speed? Relate it to linear speed. (2 marks)

Why can motion in a plane with constant acceleration be treated as two independent straight-line motions? (2 marks)

What is the maximum height of a projectile thrown vertically up at 20 m/s? Take g = 10 m/s^2. (2 marks)

A particle starts from the origin at t = 0 with velocity 10j m/s and moves with acceleration (8i + 2j) m/s^2. Find its y-coordinate when its x-coordinate is 16 m, and its speed at that time. (3 marks)

A ball is thrown horizontally at 10 m/s from the top of a cliff 45 m high. Find the speed of the ball when it hits the ground. Take g = 10 m/s^2. (3 marks)

A body moves in a circle of radius 2 m with a speed of 4 m/s. Find its angular speed and centripetal acceleration. (3 marks)

Find the angle between A = i + j and the x-axis. (3 marks)

A projectile has range 40 m and time of flight 2 s. Find its horizontal velocity. (3 marks)

Read the passage and answer the questions. A footballer kicks a ball at 25 m/s at 37 degrees above the ground. Take sin 37 = 0.6, cos 37 = 0.8 and g = 10 m/s^2. (i) Find the horizontal and vertical components of the velocity. (ii) Find the time of flight. (iii) Find the horizontal range. (5 marks)

Read the passage and answer the questions. A long jumper leaves the ground at 9 m/s at 45 degrees. Take g = 10 m/s^2. (i) Find the range of the jump. (ii) Find the maximum height reached. (iii) Why do athletes try to take off at about 45 degrees? (5 marks)

Read the passage and answer the questions. A child sits on a merry-go-round 3 m from the centre. It completes one revolution every 6 s. (i) Find the angular speed. (ii) Find the linear speed of the child. (iii) Find the centripetal acceleration. (5 marks)

Read the passage and answer the questions. A plane flying horizontally at 100 m/s at a height of 500 m drops a food packet. Take g = 10 m/s^2. (i) Find the time for the packet to reach the ground. (ii) Find its horizontal distance from the drop point. (iii) Where is the plane when the packet lands, if its velocity is unchanged? (5 marks)

Read the passage and answer the questions. Two forces act on a boat: 6 N towards the east and 8 N towards the north. (i) Write them in vector form using i and j. (ii) Find the magnitude of the resultant. (iii) Find its direction with respect to east. (5 marks)

Explain the addition of vectors by the graphical and analytical methods, using the resolution of vectors into components. (6 marks)

Explain motion in a plane with constant acceleration and derive the vector equations of motion. (6 marks)

Derive the equation of the trajectory of a projectile and show that it is a parabola. (6 marks)

Derive the expressions for the maximum height, time of flight and horizontal range of a projectile, and show that the range is maximum at 45 degrees. (6 marks)

Explain uniform circular motion. Derive a = v^2/r = omega^2 r and give two examples from daily life. (6 marks)