Velocity
What is the vertical velocity at the peak of a projectile's trajectory?
Zero
An object has a horizontal velocity of 6 m/s to the right and a vertical velocity of 9 m/s. What is its overall velocity, and what angle is it aimed at?
Overall velocity = 10.81 m/s (use Pythagorean theorem)
Angle = 56.3o (use trig - tan-1(9/6)= 56.3)
What force influences vertical motion?
Gravity
A quarterback throws a football in the air with an initial velocity of 19 m/s at an angle of 32o. If his receiver catches it after 4.2 seconds, how long did it take for the ball to reach its maximum height?
2.1 seconds
What is the name for the shape of a projectile's motion?
Parabola
If a ball is thrown straight up with a velocity of 5.8 m/s, what will its velocity be right before it hits the ground?
-5.8 m/s
True/False. The horizontal velocity is affected by gravity.
FALSE
TRUE/FALSE. The vertical velocity is unaffected by the horizontal velocity.
TRUE - vertical and horizontal motion occur independently
A water balloon launcher fires with an initial velocity of 25 m/s at an angle of 38 degrees. If the water balloon reaches its maximum height after 1.57 seconds, how far away does it land?
61.8 m
How much time would it take for a pencil to fall off of a desk that is 0.98 meters tall?
0.45 seconds
An object is launched with an initial vertical velocity of 50 m/s and a horizontal velocity of 30 m/s. At the top of its arc, what are the values of horizontal and vertical velocity?
Horizontal = still 30 m/s (no acceleration)
Vertical = 0 m/s (no longer moving up)
A ball is tossed upwards and momentarily stops at its highest point. Describe the ball's vertical velocity from this point right up until it hits the ground:
It starts with zero vertical velocity and the vertical velocity gets bigger and bigger as it falls
Kate is on vacation at the Grand Canyon and drops a pebble over the edge and counts to 7.50 seconds before the pebble hits bottom. How high is the canyon?
275.6 meters
A football is kicked with an initial velocity of 20 m/s at an angle of 37 degrees. How long is it in the air?
2.46 seconds
What angle should you launch a projectile at if you want to simultaneously maximize both its distance travelled and height?
45 degrees
A golf ball is hit off the tee and has an initial velocity of 63 m/s at an angle of 31 degrees above the ground. What are its vertical and horizontal components of this velocity?
Vertical: 63sin(31) = 32.44 m/s
Horizontal: 63cos(31) = 54.0 m/s
A ball is dropped off of a 275.0 meter high office building. What is its velocity when it strikes the ground? (remember direction!)
-73.4 m/s
A football is punted upward with a velocity of 28 m/s straight up. How high is the football off the ground at its highest point?
(hint: you need to find time until the peak first)
40 m
A baseball is thrown with an initial velocity of 34 m/s at an angle of 19 degrees above the ground.
How long does it take to reach its peak, and how high off the ground will it be at this point?
It will reach the peak after 1.13 seconds and will be 6.25 m high.
A plane is flying with a constant velocity. If a package is dropped out of the plane while it is moving, will the box land behind the plane, in front of the plane, or directly underneath the plane? WHY?
Directly underneath ... both have the same constant velocity, so they will travel the same horizontal distance in the same amount of time
While standing on the top of a 10 m building, Jack pushes his skateboard off the edge with an initial velocity of 3 m/s in the horizontal.
When the skateboard hits the ground 1.43 seconds later, what are its horizontal and vertical velocities?
Horizontal velocity = still 3 m/s (no acceleration in X)
Vertical velocity = -14.01 m/s
A coconut rolls horizontally off of a 8m tall cliff with an initial X velocity of 5 m/s. What is its final vertical (Y) velocity right before it hits the ground?
-12.5 m/s
A skydiver traveling at 20.0 m/s falls 80.625 meters and her speed increases to 44.5 m/s. How many seconds did it take her to fall this distance?
2.5 seconds
If a ball launched at 45 degrees reaches its peak after 3 seconds and lands 176.4 meters away from where it was thrown, what were its initial vertical and horizontal components?
Horizontal: 29.4 m/s
Vertical:29.4 m/s
You shoot a cannon horizontally from a height of 196 m. The cannonball is projected horizontally at 8.5 m/s. How far away does the cannonball land?
53.7 m