The mass of a particular eagle is twice that of a hunted pigeon. Suppose the pigeon is flying north at ₁2 = 16.5 m/s when the eagle swoops down, grabs the pigeon, and flies off. At the instant right before the attack, the eagle is flying toward the pigeon at an angle 0 = 61.9° below the horizontal and a speed of ₁,1 35.5 m/s. What is the speed up of the eagle immediately after it catches its prey? Uf = What is the magnitude of the angle, measured from horizontal, at which the eagle is flying immediately after the strike? B II m/s L
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- A soccer ball is kicked with a speed of 9.0 m/s at an angle of 25° above the horizontal. Write the ball's velocity in terms of rectangular unit vectors, using the standard notation that î is horizontal and ĵ is vertical.You are working part-time for the GT Sports Media Complex, editing video for the women’s softball team. In one particular clip, a GT player hits a home run over the center field fence. The ball leaves the bat at a height of 4 ft, and crosses the outfield fence (220 ft away) at a height of 10 ft. Logs of the game indicate that the pitch was clocked at 68 mph as it reached the plate. Your frame-by-frame analysis of the 30-frame-per-second video indicate that the ball spent only a single frame in contact with tha bat, and another 126 frames travelling to the outfield fence. A quick internet seach tells you that a typical college softball weighs 0.4 lb. How many pounds of average force act on the ball during ocntact with the bat?Here are three vectors in meters: d1 = -6.60î + 8.70ĵ + 3.50k d 2 = - 2.00î – 4.00ĵ + 2.00k d 3 = 2.00î + 3.00ĵ + 1.00k What results from (a) đ1· ( đ 2 + đ 3 ), (b) đ 1 · ( đ 2 × đ 3), and d 1 x ( d 2 + d 3 ) (c), (d) and (e) for i,j and k components respectively)? (a) Number i Units (b) Number Units (c) Number i Units (d) Number Units (e) Number i Units
- Dr. Jekyll (m = 70kg) is riding a skateboard when he realizes the cranberry juice he’s drinking is sweetened with artificial sweetener and turns into Mr. Hyde (m = 155kg). If Dr. Jekyll was initially moving at 6.5m/s, what is Mr. Hyde’s speed? (assume no external forces act)On planet #3, you fire a projectile horizontally from the edge of a vertical cliff 76.0 m above the ground, with an initial speed of 31.2 m/s. The projectile lands 71.5 m away from the base of the cliff. What is the value of g for planet #3? 848.50 m/s^2 28.94 m/s^2 14.47 m/s^2 12.05 m/s^2An constant applied force of 40.1 N lifts an 2.50 kg mass straight up, resulting in a final speed of 3.6 m/s. What distance did the mass move if it was initially at rest?
- A child riding a bicycle has a total mass of 30.6 kg. The child approaches the top of a hill that is 27.9 m high 27.9 and is 86.8 m (ℓ) long at 12.1 m/s. If the force of friction between the bicycle and the hill is 26.7 N, what is the child's velocity at the bottom of the hill? (Disregard air resistance, g = 9.8 m/s2.)2.3. A train car is sitting on a level track when a second car moves in. The second car hits the first, their hitches engage, and they move together. Both cars have equal masses of about 120 000 kg, and the second car initially has a velocity of 1.5 m/s. (a) Draw a diagram that illustrates the situation and include an arrow representing the velocity vector of the second car and a separate arrow representing ĉ, the unit vector for the coordinate system along the tracks. (b) Write vector expressions for both the velocity and momentum of the second car using at least two forms of vector notation that have been covered in class. (c) Just before the collision, what is the velocity of the center of mass of the system that includes both cars? Again, express this as a vector. (d) Just before the collision, what is the total kinetic energy of the system that includes both cars?At a particular instant, a hot air balloon is 48.7m above a horizontal field and descending at a rate of 2.67m/s. At this instant, a girl who is riding in the gondola of the balloon throws a ball with a speed of 14.7m/s with a direction that is horizontal in the frame of the gondola. When the balloon lands on the ground, how far, in meters, is she from where the ball landed? Neglect air resistance.
- How would I begin to solve this problem? In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by y(t) = (RE3/2 + 3*(g/2)1/2 REt)2/3 where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)An archer shoots an 18.0-gram arrow at a 43.0-gram target on a wall 32.0 m high. If the arrow is shot at a velocity of v0 = 60.0 m/s, what is the speed of the arrow when it reaches the target?k A 13.00 kg particle starts from the origin at time zero. Its velocity as a function of time is given by = 10t² + 1tj where is in meters per second and t is in seconds. (Use the following as necessary: t.) V (a) Find its position as a function of time. ŕ= esc 10/³1 + ²/2 2²; 3 (b) Describe its motion qualitatively. The particle starts from rest at the origin, starts moving in the y direction, and gains speed faster and faster while turning to move more and more nearly parallel to the x axis. Score: 0.06 out of 0.06 Comment: (c) Find its acceleration as a function of time. a = 20ti + lj m/s² (d) Find the net force exerted on the particle as a function of time. F= T= (e) Find the net torque about the origin exerted on the particle as a function of time. N m X X (f) Find the angular momentum of the particle as a function of time. Ľ Need Help? Read It F1 N x (g) Find the kinetic energy of the particle as a function of time. K= x kg m²/s X (h) Find the power injected into the particle as a…