Small frogs that are good jumpers are capable of remarkable accelerations. One species reaches a takeoff speed of 3.7 m/s in 60 ms. What is the frog's acceleration during the jump?
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- Tired, you walk from your house to a local coffee shop to get an espresso. You average a speed of 2.4 m/s on your way there. After your espresso, you decide to run directly back to your starting point with an average speed of 5.6 m/s. Assume you spend 4 minutes at the coffee shop. If your average speed for this entire trip is 1.9 m/s, what is the distance between your house and the coffee shop?A speed skater moving to the left across frictionless ice at 7.8 m/s hits a 4.5-m-wide patch of rough ice. She slows steadily, then continues on at 6.1 m/s What is the magnitude of her acceleration on the rough ice?The engineer of an intercity train observes a rock slide blocking the train's path 550 m ahead and activates the train's emergency brakes. The train decelerates uniformly (Hint: negative acceleration) at 1.7 m/s and completely stopes just before hitting the rock. What is the initial speed of the train measured in m/s?
- A ball is hit straight up with an initial speed of 28 m/s. What is the speed of the ball 2.2 seconds after it is hit?A rock is thrown straight up into the air with an initial speed of 85 m/s at time t = 0. Ignore air resistance in this problem. At what times does it move with a speed of 13 m/s? Note: There are two answers to this problem.You are testing a jet back pack on a dummy. You start it rising with an upward acceleration of 3 m/sec/sec. after 9 seconds the jetpack fails (upward acceleration stops, gravity takes over). How fast is the dummy moving when it hits the ground?
- A commuter backs her car out of her garage with a constant acceleration of 1.9 m/s2. Assume that her initial motion is in the positive direction. How long does it take her to reach a speed of 2.35 m/s in seconds? If she then brakes to a stop in 0.65 s, what is her acceleration in meters per square second?A pole vaulter is momentarily motionless as he clears the bar, which is set 4.2 m above the ground. He then falls onto a thick cushion. The top of the cushion is 80 cm above the ground, and it compresses by 50 cm as the pole vaulter comes to rest. What is his acceleration as he comes to rest on the cushion?A rocket, initially at rest on the ground, accelerates upward with a constant acceleration of 94.0 m/s2 until it reaches a speed of 1.50E2 m/s when the engines are cut off. After that, the rocket is in free-fall. What is the maximum height reached by the rocket?
- A rocket is launched from the ground such that its net acceleration is 15 m/sec2 when the engine is on. After 10 seconds, the engine cuts off. How high does the rocket go?A cheetah at rest notices a gazelle standing at a distance of 150.0 m. At the same time the gazelle notices the cheetah. The gazelle accelerates at 2.0 m/s2 for 8.0 s, after which it has reached top speed. The cheetah accelerates at 2.5 m/s2 until it has reached its top speed of 115.2 km/h. It can only continue at this speed for 35 s. Will the cheetah catch the gazelle? If so, when and where?Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1000 m/s2 lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is 0.36 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 2.2 mm. If the floor is carpeted, this stopping distance is increased to about 1.2 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume that the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate. Hardwood floor magnitude m/s2 duration ms Carpeted floor magnitude m/s2 duration ms