Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 7, Problem 25P
To determine
To Find: The minimum initial speed of a projectile for it to reach a height of
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Find the minimum initial speed of a projectile in order for it to reach a height of 2145 km above the surface of the earth
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A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed ?esc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ?=2.93×106 g/m3 and volume ?=1.94×1012 m3 . Recall that the universal gravitational constant is ?=6.67×10-11 N·m2/kg2 .vesc = ? m/s
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Physics Fundamentals
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- An uncrewed mission to the nearest star, Proxima Centauri, is launched from the Earth's surface as a projectile with an initial speed of 43.1 km/s, just enough for the spacecraft to escape the Earth's gravity and leave the solar system. Ignoring air resistance and the Earth's rotation, what is the speed of the spacecraft when it is more than halfway to the star? Assume we are ignoring the effect of the Sun on the spacecraft.arrow_forwardA bowling ball of mass m = 1.6 kg is resting on a spring compressed by a distance d = 0.36 m when the spring is released. At the moment the spring reaches its equilibrium point, the ball is launched from the spring into the air in projectile motion at an angle of θ = 38° measured from the horizontal. It is observed that the ball reaches a maximum height of h = 3.5 m, measured from the initial position of the ball. Let the gravitational potential energy be zero at the initial height of the bowling ball. a. What is the spring constant k, in newtons per meter? b. Calculate the speed of the ball, vo in m/s, just after the launch.arrow_forwardA team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed vesc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ? = 2.67 × 106 g/m3 and volume V =1.71 × 1012 m3. Recall that the universal gravitational constant is G = 6.67 × 10-11 (Nm2)/(kg2).arrow_forward
- In his novel From the Earth to the Moon Jules Verne first suggested that it might be possible to travel to the moon by firing a very high velocity projectile at the moon. Find the minimum initial velocity of such a projectile as it leaves earth's atmosphere. Take into account the moon's gravitational force.arrow_forwardYou are designing a single-stage rocket to launch a 300-kg satellite. Assume the rocket engine's I, as 460 sec. Use g=9.8 m/sec² for the gravity acceleration constant. sp (a) Assume that you are launching the satellite in free space with no gravity and no aerodynamic drag, and your rocket has zero mass except the pronellants and the satellite. Calculate the mass of the propellants to give AV = 7.784 km/sec. (b) Assume the same in (a) except that the rocket's mass is proportional to the propellants: 15% of the propellants. Calculate the mass of the propellants for AV=7.784 km/sec. (Of course, the rocket's mass remains the same after the burn)arrow_forwardA 76.0 kilogram boulder is sliding horizontally at the top of a 20-meter-high vertical cliff over the surface of a lake. The top of a dam's vertical face is 100 meters from the cliff's base, with the dam's top level with the surface of the lake's water. A level plain is 25 meters below the dam's crest. (a) What must be the lowest speed of the rock as it exits the cliff in order for it to reach the plain without colliding with the dam? (a) How far does the rock reach the plain from the dam's foot?arrow_forward
- Let us consider the fall of a pole vaulter as a projectile once he releases the pole. The pole has a lake of 15 8 feet and once the athlete releases the pole he will find a mattress 2 feet high, 10 feet wide and 16 feet long, which protects him in the fall. If an athlete lets go of the pole when it was 13.7 ft above the ground with a speed of 15.7 ft/s at an angle of 73 degrees. Enter the horizontal distance that the athlete will travel with the indicated conditions, add the units in the resultarrow_forwardAn object is projected from the surface of the earth with a speed of 2.72×104 m/s. What is its speed when it is very far from the earth? (Neglect air resistance.)arrow_forwardIf a projectile is fired straight up from the earth’s surface, what would happen if the total mechanical energy (kinetic plus potential) is (a) less than zero, and (b) greater than zero? In each case, ignore air resistance and the gravitational effects of the sun, the moon, and the other planets.arrow_forward
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