2D Motion

How long is the ball in the air?

• 3s

• 4s

• 5s

• 6s

Answer explanation

In trajectory problems we assume the displacement is zero (since the ball travels up and then falls back down)

If the initial vertical velocity is Viy = 30 m/s and the acceleration due to gravity is -10 m/s^2.

y = Viy(t) + 1/2a(t^2)

0 = 30 m/s (t) + 1/2 (-10 m/s^2)(t^2)

0 = 30 m/s(t) - 5m/s^2(t^2)

5 m/s^2(t^2) = 30 m/s(t)

t = 6s

A boat travels across a 200 meter wide river. The boat is travelling at 8 m/s and is travelling straight across the river. The river's current is 2 m/s.

How long does it take for the boat to cross the river?

• 15 s

• 20 s

• 25 s

• 30 s

Answer explanation

The distance formula is

x = Vix(t) where x is the distance, Vix is the velocity on the x axis and t is time

Filling in the knowns:

200 m = 8 m/s (t)

Divide both sides by 8

25 = t

A boat travels across a 200 meter wide river. The boat is travelling at 8 m/s and is travelling straight across the river. The river's current is 2 m/s.

How far does the boat travel down the river?

• 40 m

• 50 m

• 60 m

• 80 m

Answer explanation

The boat takes 25 seconds to cross the river

x = Vix (t) 200 = 8 m/s (t)

divide both sides and we get

25s = t

If the current is 2 m/s this will push our boat 2 meters per second for 25 seconds

y = Viy (t) y = 2 m/s (25)

y = 50m

The cow travels 10 m north, 20 m east, 30 m south and 10 m west.

What is the displacement of the cow?

• 22 m down and to the right

• 22 m down and to the left

• 50 m up and to the right

• 50 m up and to the left

Answer explanation

On the y axis the cow moves

10 north and 30 south or

y = +10 - 30 for -20

On the x axis the cow moves

20 east and 10 west or

x = +20 -10 for +10

So the cow would move -20 south and +10 north

a^2 + b^2 =c^2

20^2 + 10^2 = c^2

400 + 100 = c^2 or c^2 = 500

Square root for for c = 22.3

An object that is traveling east at a constant rate has

• velocity, but neither acceleration nor speed.

• speed, but neither velocity nor acceleration.

• speed and velocity, but no acceleration.

• acceleration and speed, but no velocity.

A dog and a cat are about to fight, running towards each other, both at 12 m/s. What are their velocities relative to each other?

• 12 m/s

• 24 m/s

• 0 m/s

• 6 m/s

Tags

NGSS.MS-PS2-1

A train is moving at a velocity of 15 m/s East. A passenger at the back of a train throws a baseball with a speed of 15 m/s West. What is the velocity of the baseball relative to the ground? (In other words: how fast does a person on the ground see the ball move?)

• 30 m/s East

• 15 m/s West

• 0 m/s

• 30 m/s West

Tags

NGSS.MS-PS3-1

NGSS.MS-PS3-5

What happens to the magnitude of acceleration?

• It remains the same

• Decreases then increases

• Increases then decreases

• Increases the entire time

Answer explanation

The only acceleration acting upon the object in flight is gravity which is constant throughout the flight

Tags

NGSS.MS-PS2-2

A nerf dart is fired at an 45 degree angle. The dart flies over the classroom then lands upon the floor.

What happens to the magnitude of the vertical component of velocity?

• It remains the same

• Decreases then increases

• Increases then decreases

• Increases the entire time

Answer explanation

As the dart goes up the vertical velocity is being effected by gravity. It starts out positive so it is being decreased by gravity until it reaches zero (when it is at the zenith of flight) then it begins to increase in the negative direction.

A ball rolls off a 1 meter tall table. What happens to the horizontal and vertical velocity as it travels towards the ground

• horizontal velocity increases and vertical velocity stays the same

• horizontal velocity increases and vertical velocity increases

• horizontal velocity increases and vertical velocity decreases

• horizontal velocity stays the same and vertical velocity increases

Answer explanation

As the ball rolls off the table it has no horizontal acceleration so the horizontal velocity stays the same but the vertical velocity is effected by gravity so it increases