A ball is launched from (0, 0, 8) towards a target on the x-axis at (20, 0, 0). The initial velocity is <5, 0, K> and the only acceleration is due to gravity (to simplify calculations, use a = <0, 0, −10>). Whatshould we choose for the value of K in the velocity so that the ball hits the target

On a planet very similar to Earth, but slightly denser, where acceleration due to gravity is 10 m/s2, a projectile is fire vertically from a height of 100 meters with an initial velocity of 40 m/s. Its position above the ground after t seconds is given by h(t) = 100 + 40t − 5t2 meters. Find the maximum height the projectile attains.

The position F of a particle moving in an xy plane is given by: F=(200*-5.002)i + (6.00–7.00*)} with F in meters and t in seconds. (Note that this is an example where the units for the coefficients are ignored – don't let this distract you!) In unit vector notation, calculate: а). г b). й с). а for time t= 2.00 s. %3D d). What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t= 2.00 s?

A ball is thrown horizontally from the top of a building 74 m high. The ball strikes the ground at a point 90 m horizontally away from and below the point of release. What is the speed of the ball just before it strikes the ground? (note: speed is magnitude of velocity at that point).

2. Your friend is on the top of a sheer vertical cliff 14 meters high and you are on the ground below. Your friend throws a ball at an angle of 49° above the horizontal, and with an initial speed of 9.2 m/s. How long is the ball in the air? How far from the base of the cliff should you be in order to catch the ball1? Neglect air resistance. (The situation is as shown in Fig. 6.3.) 3. Starting from rest, a 62 g ball rolled down the tube like the one to be used during this experiment and stopped exactly at the exit. The initial and final ends of the tube were 109 Ocm and 101 cm above the floor, respectively. What was the frictional energy loss? If the tube is rotated so that the heights of the ends of the tube are now 124 cm and 88 cm above the floor, what is the exit velocity of the ball? 4. If the ball in the latter part of Problem 3 leaves the tube at an angle of 25° from the horizontal, what is its time of flight and range? 5. What would be the answers to Problem 4 if there were no…

On a planet very similar to Earth, but slightly denser, where acceleration due to gravity is 10 m/s2, a projectile is fire vertically from a height of 100 meters with an initial velocity of 40 m/s. Its position above the ground after t seconds is given by h(t) = 100 + 40t − 5t2 meters.find the velocity of the projectile as it hits the ground

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.)

A lunar lander is descending toward the moon's surface. Until the lander reaches the surface, its height above the surface of the moon is given by y(t) = b – ct + dt², where b = 800 m is the initial height of the lander above the surface, c = 60.0 m/s, and d = 1.05 m/s². Calculate for the: (a) initial position of the lander; (b) initial velocity of the lander; and (c) initial acceleration of the lander.

In a naval battle, a battleship is attempting to fire on a frigate. The battleship is a distance d₁ = 2,200 m to the east of the peak of a mountain on an island, as shown in the figure below. The frigate is attempting to evade cannon shells fired from the battleship by hiding on the west side of the island. The initial speed of the shells that the battleship fires is v, = 245 m/s. The peak of the mountain is h = 1,640 m above sea level, and the western shore of the island is a horizontal distance d₂ = 290 m from the peak. What are the distances (in m), as measured from the western shore of the island, at which the frigate will be safe from fire from the battleship? (Note the figure is not to scale. You may assume that the height and width of the frigate are small compared to d, and h.) less than m, or more than d₁ m 4

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