A trap-jaw ant snaps its mandibles shut at very high speed, a good trait for catching small prey. But an ant can also slam its mandibles into the ground; the resulting force can launch the ant into the air for a quick escape. A 12 mgmg ant hits the ground with an average force of 47 mNmN for a time of 0.13 msms; these are all typical values.

Two objects (m, = 4.50 kg and m, = 3.30 kg) are connected by a light string passing over a light, frictionless pulley as in the figure below. The 4.50-kg object is released from rest at a point h = 4.00 m above the table. (a) Determine the speed of each object when the two pass each other. m/s (b) Determine the speed of each object at the moment the 4.50-kg object hits the table. m/s (c) How much higher does the 3.30-kg object travel after the 4.50-kg object hits the table? Need Help? Read It

A 6.0 ✕ 104 kg space probe is traveling at a speed of 12000 m/s through deep space. Retrorockets are fired along the line of motion to reduce the probe's speed. The retrorockets generate a force of 3.0 ✕ 105 N over a distance of 2400 km. What is the final speed of the probe? m/s

A railroad cart with a mass of m₁ = 12.6 t is at rest at the top of an h = 10.3 m high hump yard hill. m m₂ h After it is pushed very slowly over the edge, it starts to roll down. At the bottom it hits another cart originally at rest with a mass of m₂ = 18.6 t. The bumper mechanism locks the two carts together. What is the final common speed of the two carts? (Neglect losses due to rolling friction of the carts. The letter t stands for metric ton in the SI system.)

Gayle runs at a speed of 3.65 m/s and dives on a sled, initially at rest on the top of a frictionless snow-covered hill. After she has descended a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back and together they continue down the hill. What is their speed at the bottom of the hill if the total vertical drop is 15.0 m? Gayle's mass is 48.0 kg, the sled has a mass of 5.45 kg and her brother has a mass of 30.0 kg. m/s

A baseball has a mass of 0.140 kg, and it is pitched towards home plate at a speed of 48.0 m/s. Assume that the ball is pitched horizontally and that the ball is hit horizontally back in the opposite direction. If the bat exerts an average force of 9100 N for 2.80 ms, what is the final speed of the ball in m/s?

Figure P7.44 45. Review. Two constant forces act on an object of mass m = QIC 5.00 kg moving in the xy plane as shown in Figure P7.45. Force F, is 25.0 N at 35.0°, and force F, is 42.0 N at 150°. At time t = 0, the object is at the origin and has velocity (4.00î + 2.50j) m/s. (a) Express the two forces in unit-vector notation. Use unit-vector notation for your other answers. (b) Find the total force exerted on the object. (c) Find the object's acceleration. Now, considering the instant t = 3.00 s, find (d) velocity, (e) its position, its kinetic energy the object's (f) from mv, and (g) its F2 F kinetic from 150° energy mu + EF · A. (h) What conclusion can you draw by comparing the answers to parts (f) and (g)? 35.0° m Figure P7.45

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A 66.0-kg athlete leaps straight up into the air from a trampoline with an initial speed of 7.5 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? This answer has not been graded yet. (b) Select the height at which the athlete's speed is 7.5 m/s as  y = 0.  What is her kinetic energy at this point? JWhat is the gravitational potential energy associated with the athlete? J(c) What is her kinetic energy at maximum height? JWhat is the gravitational potential energy associated with the athlete? J(d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. m(e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer. m/s

Gayle runs at a speed of 3.60 m/s and dives on a sled, initially at rest on the top of a frictionless snow - covered hill. After she has descended a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back and together they continue down the hill. What is their speed at the bottom of the hill if the total vertical drop is 15.0 m? Gayle's mass is 46.5 kg, the sled has a mass of 5.10 kg and her brother has a mass of 30.0 kg.