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1. Which of the following descriptions of moving objects accurately portray a projectile? List all that apply.
a. an object which is moving through the air and not touching any surface
b. a falling skydiver with an open parachute
c. any object upon which air resistance is negligible
d. a free-falling object
e. an object upon which the only significant force is the force of gravity
f. a falling feather
g. a falling feather in a vacuum chamber
h. a falling feather in a falling vacuum chamber.
2. An airplane that flies at 100 km/h in a 100 km/h hurricane crosswind has a speed (relative to the ground) of ____.
a. 0 km/h b. 100 km/h c. 141 km/h d. 200 km/h
3. The launch velocity and angle is given for three different projectiles. Use trigonometric functions to resolve the velocity vectors into horizontal and vertical velocity components. Then use kinematic equations to determine the time that the projectile is in the air, the height to which it travels (when it is at its peak), and the horizontal distance that it travels. (To simplify the calculations, use an acceleration of gravity value of -10 m/s/s.)
a. Given: Launch Vel. = 30.0 m/s Launch angle = 30.0 degrees | b. Given: Launch Vel. = 30.0 m/s Launch angle = 45.0 degrees | c. Given: Launch Vel. = 30.0 m/s Launch angle = 50.0 degrees |
Calculate: vix = 26.0 m/s viy = 15 m/s tup = 1.5 s ttotal = 3.0 s y at peak = 11.3 m x = 77.9 m | Calculate: vix = 21.2 m/s viy = 21.2 m/s tup = 2.12 s ttotal = 4.24 s y at peak = 22.5 m x = 89.9 m | Calculate: vix = 21.2 m/s viy = 21.2 m/s tup = 2.12 s ttotal = 4.24 s y at peak = 22.5 m x = 89.9 m |
4. If a projectile is launched horizontally with a speed of 12.0 m/s from the top of a 24.6-meter high building. Determine the horizontal displacement of the projectile.
5. Two physics students stand on the top of their 3.29-meter second-story deck and launch a water balloon from a home-made winger. The balloon is launched upward at a speed of 45.2 m/s and an angle of 39.1 degrees. The balloon lands in a retention pond whose surface is 2.92 meters below grade. Determine the horizontal distance from launch location to landing location.
6. A place kicker kicks a football from 39.6 meters from the goal posts. The kick leaves the ground with a speed of 24.8 m/s at an angle of 49.6 degrees. The goal posts are 3.10-meters high.
(a) Determine the amount by which the kick clears the goal posts.
(b) For this given launch velocity, what is the longest field goal (in yards) which could have been kicked? Assume that the football hits the horizontal cross-bar of the posts and bounces through. Given: 1.00 meter = 3.28 feet.
7. An airplane starts at Point A and flies 210 km at 311 degrees to Point B. The plane then flies 179 km at 109 degrees to Point C. Finally, the plane flies 228 km at 29.0 degrees to Point D. Determine the resulting displacement (magnitude and direction) from Points A to D.
8. An unfortunate accident occurred on the tollway. A driver accidentally passed through a faulty barricade on a bridge (quite unfortunately). and landed in a pile of hay (quite fortunately). Measurements at the accident scene reveal that the driver plunged a vertical distance of 8.26 meters. The car carried a horizontal distance of 42.1 meters from the location where it left the bridge. If the driver was in a 65 mi/hr speed zone, then determine the amount by which the driver was exceeding the speed limit at the time of the accident. Assume that the contact with the barricade did not slow the car down. (1.00 m/s = 2.24 mi/hr)
9. 72. A car is parked on a cliff overlooking the sea. The cliff is inclined at an angle of 29.0 degrees below the horizontal. The negligent driver leaves the car in neutral and it begins rolling from rest towards the cliff's edge with an acceleration 4.50 m/s/s. The car moves a linear distance of 57.2 m to the edge of the cliff before plunging into the ocean below. The cliff is 42.2 m above the sea.
(a) Find the speed (in m/s) of the car the moment it leaves the cliff.
(b) Find the time (in seconds) it takes the car to drop to the water below the edge of the cliff.
(c) Find the position (in meters) of the car relative to the base of the cliff when it lands in the sea.
10. The formula h (t) = -16 t 2 + 32 t + 80 gives the height h above ground, in feet, of an object thrown, at t = 0, straight upward from the top of an 80 feet building.
a - What is the highest point reached by the object?
b - How long does it take the object to reach its highest point?
c - After how many seconds does the object hit the ground?
d - For how many seconds is the hight of the object higher than 90 feet?
a - What is the highest point reached by the object?
b - How long does it take the object to reach its highest point?
c - After how many seconds does the object hit the ground?
d - For how many seconds is the hight of the object higher than 90 feet?
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