Motion in Two or Three Dimensions

Examples of solutions

Problem 1

A squirrel has x - and y - coordinates (2.7 m, 3.8 m) at time t₁ = 0 and coordinates (-4.1 m, 6.8 m) at time t₂ = 4.0 s. For this time interval, find
a) the components of the average velocity;
b) the magnitude and direction of the average velocity.

Problem 2

An elephant is at the origin of coordinates at time t₁ = 0. For the time interval from t₁ = 0 to t₂ = 20.0 s the average velocity of the elephant has components (v_av)_x = 4.2 m/s and (v_av)_v = -5.6 m/s. At time t₂ = 20.0 s,
a) what are the x - and y - coordinates of the elephant?
b) how far is the elephant from the origin?

Problem 3

A jet Plane at time t₁ = 0 has components of velocity v_x = 160 m/s, v_y = -80 m/s. At time t₂ = 20.0 s the velocity components are v_x = 110 m/s, v_y = 60 m/s.
a) Sketch the velocity vectors at t₁ and t₂ - How do these two vectors differ? For this time interval, calculate
b) the components of the average acceleration;
c) the magnitude and direction of the average acceleration.

Problem 4

A dog running in an open field has components of velocity v_x =3.8 m/s and v_y = 2.6 m/s at t₁ = 10.0 s. For the time interval from t₁ = 10.0 s to t₂ = 20.0 s, the average acceleration of the dog has magnitude 0.55 m/s² and direction 52.0° measured from the +x - axis toward the +y - axis. At t² = 20.0 s,
a) what are the x - and y - components of the dog's velocity?
b) what are the magnitude and direction of the dog's velocity?
c) Sketch the velocity vectors at t¹ and t². How do these two vectors differ?

Problem 5

A tennis ball rolls off the edge of a table top 1.00 m above the floor and strikes the floor at a point 2.80 m horizontally from the edge of the table. Air resistance may be ignored,
a) Find the time of flight, b) Find the magnitude of the initial velocity, c) Find the magnitude and direction of the velocity of the ball just before it strikes the floor. Draw a diagram to scale.

Problems for solution without assistance

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