A jet landing on an aircraft carrier. In a later maneuver, the jet comes in for a landing on solid ground with a speed of 100 m/s, and its acceleration can have a maximum magnitude of 5.00 m/s2 as it comes to rest. (a) From the instant the jet touches the runway, what is the minimum time interval needed before it can come to rest? (b) Can this jet land at a small tropical island airport where the runway is 0.800 km long? (c) Explain your answer.

Two small children are riding toward each other along the x axis on their tricycles. At time t = 0 the first child is located at the origin and travels with a constant speed v₁ in the +x direction. Also at t 0 the second child starts from rest at x = d and accelerates in the - direction with acceleration a(t) = −c₁t, where c₁ is a positive constant. (i) Derive an equation that could be solved to find the time at which the two children collide. (ii) If the time of impact in part (i) is denoted by t*, how fast will the second child be traveling at the time of impact? - Law Application V1 x = 0 x = d X

Two soccer players start from rest, 39 m apart. They run directly toward each other, both players accelerating. The first player's acceleration has a magnitude of 0.48 m/s². The second player's acceleration has a magnitude of 0.49 m/s². (a) How much time passes before the players collide? (b) At the instant they collide, how far has the first player run? (a) Number M. (b) Number i Units Units ✪

Objects in free fall on the earth have acceleration ay = -9.8 m/s2. On the moon, free-fall acceleration is approximately 1/6 of the acceleration on earth. This changes the scale of problems involving free fall. For instance, suppose you jump straight upward, leaving the ground with velocity νi and then steadily slowing until reaching zero velocity at your highest point. Because your initial velocity is determined mostly by the strength of your leg muscles, we can assume your initial velocity would be the same on the moon. But considering the final equation in Synthesis 2.1 we can see that, with a smaller free-fall acceleration, your maximum height would be greater. The following questions ask you to think about how certain athletic feats might be performed in this reduced-gravity environment. If an astronaut can jump straight up to a height of 0.50 m on earth, how high could he jump on the moon?A. 1.2 m            B. 3.0 m              C. 3.6 m               D. 18 m

A girl operates a radio-controlled model car in a vacant parking lot. The girl drives a car in a straight line so that the x coordinate is defined by the relation is given by x(t) = 0.5t3 – 3t2 + 3t +2 where x is in meters and t in seconds. When is the instantaneous acceleration zero?

When the effect of aerodynamic drag is included, the y-acceleration of a baseball moving vertically upward is au = -g - kv², while the acceleration when the ball is moving downward is ad=-g+kv², where k is a positive constant and v is the speed in meters per second. If the ball is thrown upward with an initial speed of 40 m/s, determine the time tu from ground to apex and the time to from apex to ground. Take k to be 0.006 m¹ and assume that g is constant. au=-g-kv² Answers: tu = td = i i 40 m/s ad=-g+kv² S S h

You are designing a weather rocket that is to be launched from rest, vertically upward off the ground. The engine burn will last for 2.5 s. If the positive y direction is upward, away from the ground, then the acceleration during the engine burn (including the influence of gravity) is ay(t)=bt^3 with b = 16.79 m/s^5 and t the time from engine ignition. After the engine burns out, the acceleration is then ay(t)=−g. How long after the engine burns out does the rocket take to reach its maximum height?

In a local diner, a customer slides an empty coffee cup down the counter for a refill. The cup slides off the counter and strikes the floor at distance d from the base of the counter. (a) If the height of the counter is h, find an expression for the time t it takes the cup to fall to the floor in terms of the variables h and g. t =        (b) With what speed does the mug leave the counter? Answer in terms of the variables d, g, and h. v1 =        (c) In the same terms, what is the speed of the cup immediately before it hits the floor? v2 =        (d) In terms of h and d, what is the direction of the cup's velocity immediately before it hits the floor? ? =         radians

(a) What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 10.7 m/s when going down a slope for 4.81 s? (b) How far does the skier travel in this time?

A rocket car is traveling at a constant speed of 250 km/h on a salt flat. The driver gives the car a reverse thrust, and the car experiences a continuous and constant deceleration of 8.25 m/s^2. How much time elapses until the car is 175 m from the point where the reverse thrust is applied? Describe the situation for your answer.