1- Starting from home, you bicycle 26kmkm north in 2.7hh and then turn around and pedal straight home in 1.7hh . What are your (a) displacement at the end of the first 2.7hh , (b) average velocity over the first 2.7hh , (c) average velocity for the homeward leg of the trip, (d) displacement for the entire trip, and (e) average velocity for the entire trip?
2- A space shuttle's main engines cut off 7.9minmin after launch, at which time the shuttle's speed is 7.9km/skm/s .
What is the shuttle's average acceleration during this interval?
1- Starting from home, you bicycle 26 kmkm north in 2.7 hh and then turn around and pedal straight home in 1.7 hh . What are your (a) displacement at the end of the first 2.7 hh , (b) average velocity over the first 2.7 hh , (c) average velocity for the homeward leg of the trip, (d) displacement for the entire trip, and (e) average velocity for the entire trip? 2- A space shuttle's main engines cut off 7.9 minmin after launch, at which time the shuttle's speed is 7.9 km/skm/s . What is the shuttle's average acceleration during this interval? 3- A model rocket leaves the ground, heading straight up at 53 m/sm/s . What's its maximum altitude?, Find its velocity at 1 ss?, Find its altitude at 1 sec?, Find its velocity at 4 sec? Find its altitude at 4 ss? Find its velocity at 7 sec?, Find its altitude at 7 ss? 4- A Frisbee is lodged in a tree branch 6.1 mm above the ground. A rock thrown from below must be going at least 3.0 m/sm/s to dislodge the Frisbee. How fast must such a rock be thrown upward if it leaves the thrower's hand 1.3 mm above the ground? 5- A rock is thrown directly upward from the edge of the roof of a building that is 56.6 meters tall. The rock misses the building on its way down, and is observed to strike the ground 4.00 seconds after being thrown. Neglect any effects of air resistance. With what speed was the rock thrown? 6- You allow yourself 32 minmin to drive 21 mimi to the airport, but you're caught in heavy traffic and average only 25 mi/hmi/h for the first 20 minmin . What must your average speed be on the rest of the trip if you're to make your flight? 7- You can run 9.8 m/sm/s , 20%% faster than your brother. How much head start should you give him in order to have a tie race over 80 mm ? 8- Amtrak's 20th-Century Limited is en route from Chicago to New York at 100 km/hkm/h when the engineer spots a cow on the track. The train brakes to a halt in 1.1 minmin , stopping just in front of the cow. What is the magnitude of the train's acceleration? What's the direction of the acceleration? How far was the train from the cow when the engineer first applied the brakes? 9- You're an investigator for the National Transportation Safety Board, examining a subway accident in which a train going at 86 km/hkm/h collided with a slower train traveling in the same direction at 20 km/hkm/h . Your job is to determine the relative speed of the collision, to help establish new crash standards. The faster train's "black box" shows that it began negatively accelerating at 2.2 m/s2m/s2 when it was 50 mm from the slower train, while the slower train continued at constant speed. 10- You and your roommate plot to drop water balloons on students entering your dorm. Your window is 20 mm above the sidewalk. You plan to place an X on the sidewalk to mark the spot a student must be when you drop the balloon. You note that most students approach the dorm at about 3 m/sm/s . How far from the impact point do you place the X? 11- An ice skater is gliding along at 2.5 m/sm/s , when she undergoes an acceleration of magnitude 1.2 m/s2m/s2 for 3.0 ss. After that she's moving at 6.1 m/sm/s Find the angle between her acceleration vector and her initial velocity vector. 12- An object is moving in the xxx-direction at 1.6 m/sm/s when it undergoes an acceleration a⃗ =0.42j^m/s2a→=0.42j^m/s2. Find its velocity vector after 5.0 sec. 13- The position of an object as a function of time is r⃗ =(r→=(3.2t+t+ 1.2 t2)i^+(t2)i^+(1.7t−t− 1.6 t2)j^mt2)j^m, where tt is the time in seconds. Find the object’s magnitude of the acceleration, What is the direction of the acceleration? 14- A flock of geese is attempting to migrate due south, but the wind is blowing from the west at 5.3 m/sm/s If the birds can fly at 7.4 m/sm/s relative to the air, what direction should they head? 15- An arrow fired horizontally at 45 m/sm/s travels 24 mm horizontally, before landing on the ground. From what height above the ground was it fired? 16- A particle leaves the origin with initial velocity v⃗ o=9.0i^+17j^m/sv→o=9.0i^+17j^m/s, undergoing constant acceleration a⃗ =−0.90i^+0.21j^m/s2a→=−0.90i^+0.21j^m/s2.When does the particle cross the y-axis? What's its y-coordinate at the time? How fast is it moving? In what direction is it moving? 17- You throw a baseball at a 45∘∘ angle to the horizontal, aiming at a friend who's sitting in a tree a distance hh above level ground. At the instant you throw your ball, your friend drops another ball. The two balls will collide, no matter what your ball's initial speed, provided it's greater than some minimum value. Find an expression for that minimum speed. 18- In a chase scene, a movie stuntman runs horizontally off the flat roof of one building and lands on another roof 2.0 mm lower. If the gap between the buildings is 4.8 mm wide, how fast must he run to cross the gap? 19- A soccer player can kick the ball 33 mm on level ground, with its initial velocity at 42 ∘∘ to the horizontal. At the same initial speed and angle to the horizontal, what horizontal distance can the player kick the ball on a 18 ∘∘ upward slope? 20- A diver leaves a 3-mm board on a trajectory that takes her 2.6 mm above the board and then into the water 2.7 mm horizontally from the end of the board. At what speed did she leave the board? At what angle did she leave the board?