Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 6, Problem 52P
To determine
The velocity vector as function of time; to show that explicit integral of
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One strategy in a snowball fight is to throwa snowball at a high angle over level ground.While your opponent is watching this firstsnowball, you throw a second one at a lowangle timed to arrive before or at the sametime as the first one. Assume both snowballsare thrown with a speed of 14.3 m/s. The firstone is thrown at an angle of 73◦ with respectto the horizontal.At what angle should the second snowballbe thrown to arrive at the same point as thefirst?Answer in units of ◦
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Physics for Scientists and Engineers
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- Imagine a firework has a fuse designed so that it explodes at the highest point of its trajectory, and it's launched with an initial speed of 60 m/s at an angle of 70 degrees to the horizontal. What height h it explodes at? (Answer in cm and round-off to the whole number.)arrow_forwardGalileo's Martian descendants find that when they release balls down ramps to fly off tables that the relationship of table height h to the horizontal range of flight and the launch velocity v is h = 1.5 (3) ² They determine that releasing the ball from a 0.5-meter high ramp produces a launch velocity of around 1.9 m/s. What horizontal range before hitting the ground will the ball cover if launched off a 0.8-meter high table at this speed?arrow_forwardA railroad flatcar is traveling to the right at a speed of 13.0 m/srelative to an observer standing on the ground. Someone is riding amotor scooter on the flatcar. What is the velocity (magnitudeand direction) of the scooter relative to the flatcar if the scooter’svelocity relative to the observer on the ground is 18.0 m/s to theright?arrow_forward
- A block of mass m = 3 kg is sliding along a frictionless inclined surface that makes an angleof φφ = 300with respect to the horizontal surface.At the lowest points of the inclined surface, a projectile is fired at a speed of vv0 = 12 m/s thatmakes an angle θ0 = 450 with respect to the horizontal. Our aim of this problem is to find thetime when the projectile will hit the block. Find the time when the projectile hits the block. (Given, the initial distance between the blockand the projectile along the inclined surface at t = 0 is RR0 = 10 m as shown in the figure) Find the height h, where the projectile will hit the block.(c) Now assume that the projectile hits the block at its maximum range R along the inclinedsurface and the block is not sliding at all. Then find the maximum range along the inclinedsurface, RRmmmmmm = ?arrow_forwardA carnival game has you throw a ball through a hoop as the hoop falls from some height. Suppose for onesuch game the hoop falls from a height of 2.0 m above your hand when you throw the ball, and you stand ahorizontal distance of 3.0 m away. If you throw the ball right when the hoop is released (from rest), at whatangle must you throw the ball in order for you to win the prize?arrow_forward2.18. A ball is thrown vertially upward with an initial velocity v. The air resistance is proportional to the square of the velocity. Show that the velocity with which the ball returns to the original posi- tion is Vv, where v, is the terminal velocity.arrow_forward
- To decide who pays for lunch, a passengeron a moving train tosses a coin straight upward with an initialspeed of 5.25 m>s and catches it again when it returns to its initial level. From the point of view of the passenger, then, the coin’sinitial velocity is 15.25 m>s 2yn . The train’s velocity relative to theground is 112.1 m>s2xn . (a) What is the minimum speed of the coinrelative to the ground during its flight? At what point in the coin’sflight does this minimum speed occur? Explain. (b) Find the initial speed and direction of the coin as seen by an observer on theground. (c) Use the expression for ymax derived in Example 4-14 tocalculate the maximum height of the coin, as seen by an observeron the ground. (d) What is the maximum height of the coin fromthe point of view of the passenger, who sees only one-dimensionalmotion?arrow_forwardIn a later chapter, you will find that the weight of a particle varies with altitude such that w=mgr02r2where r0is the radius of Earth and ris the distance from Earth’s center. If the particle is fired vertically with velocity v0from Earth’s surface, determine its velocity as a function of position r. (Hint: use adr=vdv, the rearrangement mentioned in the text.)arrow_forwardCheck Your Understanding If the two golf shots in Example 4.9 were bunched at the same speed, which shot would have the greatest range? When we speak of the range of a projectile on level ground, we assume R is very small compared with the circumference of Earth. If, however, the range is large, Earth curves away below the projectile and the acceleration resulting from gravity changes direction along the path. The range is larger than predicted by the range equation given earlier because the projectile has father to fail than it would on level ground, as shown in Figure 4.17, which is based on a drawing in Newton’s Principia. If the initial speed is great enough, the projectile goes into orbit. Earth’s surface drops every 8000 m. In 1 s an object falls 5 m without a resistance. Thus, if an object is given a horizontal velocity of 8000 m/s (or 18,000 mi/hr) near Earth’s surface, it will go into orbit around the planet because, the surface continuously falls away from object Thu is roughly the speed of the Space Shuttle in a low Earth orbit when it was operational, or any satellite in a low Earth orbit. These and other aspects of orbital motion, such as Earth’s rotation, are covered in greater depth in Gravitation. Figure 4.17 Projectile to satellite. In each case shown here, a projectile is launched from a very high tower to avoid air resistance. With increasing initial speed, the range increases and becomes longer than t would be on level ground because Earth curves away beneath its path. With a speed of 8000 m/s, orbit is achieved.arrow_forward
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