Motion in a Plane — Practice

Question 1

A vector has components Ax = 3, Ay = 4. Find its magnitude and direction.

Accepted Answer

|A| = sqrt(9 + 16) = 5. Direction theta = tan^-1(4/3) = 53.13 degrees from the x-axis.

Question 2

A projectile is fired at 50 m/s at 30 degrees to the horizontal. Find T, H, and R (g = 10 m/s^2).

Accepted Answer

uy = 25 m/s. T = 2uy/g = 5 s. H = u^2 sin^2(theta)/2g = 625/20 = 31.25 m. R = u^2 sin(60)/g = 2500 x 0.866/10 = 216.5 m.

Question 3

A stone is thrown horizontally at 20 m/s from 80 m height. Find its range (g = 10 m/s^2).

Accepted Answer

Time to fall: 80 = (1/2)(10)t^2, so t = 4 s. Range = 20 x 4 = 80 m.

Question 4

A particle moves in a circle of radius 20 cm at 5 revolutions per second. Find its speed and centripetal acceleration.

Accepted Answer

omega = 2 pi f = 10 pi rad/s. v = omega R = 10 pi x 0.2 = 2 pi m/s. a_c = omega^2 R = (100 pi^2)(0.2) = 20 pi^2 m/s^2.

Question 5

What are i.j and i x j?

Accepted Answer

i.j = 0 (perpendicular unit vectors). i x j = k (right-hand rule).

Practice — Motion in a Plane