(A) Find the magnitude of the gravitational force (in N) between a planet with mass 7.75 ✕ 1024 kg and its moon, with mass 2.35 ✕ 1022 kg, if the average distance between their centers is 2.20 ✕ 108 m.     (B) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.) m/s2     (C) What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.) m/s2

A small metal ball is kicked from the edge of a cliff. Its x- and y-coordinates as functions of time are given by x = 16.7t and y = 3.64t - 4.90t2, where x and y are in meters and t is in seconds. (Do not include units in your answer.) (a) Write a vector expression for the ball's position as a function of time (in m), using the unit vectors î and ĵ. (Give the answer in terms of t.) r= By taking derivatives, do the following. (b) Obtain the expression for the velocity vector v as a function of time (in m/s). (Give the answers in terms of t.) V= a = m (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). m/s² r = m/s (d) Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the metal ball at t = 3.24 s. (Assume the position is in m, the velocity is in m/s and the acceleration is in m/s².) a = m m/s m/s²

The mass of an ear ring is 950 mg. Express this mass in Sl unit. 1. (a) 9.50 x 106 kg (b) 9.50 x 104 kg (c) 9.50 x 103 g (d) 9.50 x 101 g A 16 g steel ball and a 10 g nylon ball are dropped from the same height at the same time. As the ball 2. reaches the ground, which of the following quantity is not the same for both the balls? |(a) Displacement (b) Velocity (c) Acceleration (d) Weight. A boy pulls a table to the left with a force of 25 N. A second boy pulls the same table to the right with 3. a force of 15 N. What is the resultant force acting on the table? (a) 10 N right (b) 10 N left (c) 40 N right (d) 40 N left A driver accelerates his car and raises its speed from 40 km/h to 80 km/h. The kinetic energy of the 4. car becomes; (a) 2 times (b) 4 times (c) half (d) same The diameter of an optical fiber is 6.0 nm. Its radius in m is 5. (a) 12.0 x 106 m (b) 12.0 x 10° m (c) 3.0 x 106 m (d) 3.0 x 10° m. A swimmer completes the first 50 m of the 100-m free style in 37.8 s. On reaching…

The average distance of the earth from the sun is about 1.5 x 108 km (Figure 1). Assume that the earth's orbit around the sun is circular and that the sun is at the origin of your coordinate system. (a) Estimate the speed of the earth as it moves in its orbit around the sun. Express your answer in miles per hour with the appropriate number of significant figures. (b) Estimate the angle between the position vector of the earth now and what it will be in 4 months. (c) Calculate the distance between these two positions.

If an object is shot upward with an initial velocity, v 0, in feet per second (ft/s), the velocity, v, in ft/s is given by the formula v= v0 −32t, where t is time in seconds. Find the initial velocity of an object if the velocity after 2 seconds is 28ft/s.

A ball is thrown eastward into the air from the origin (in the direction of the positive x-axis). The initial velocity is 40 i +64 k, with speed measured in feet per second. The spin of the ball results in a southward acceleration of 4 ft/s2, so the acceleration vector is a = -4 j - 32 k. Where does the ball land? (Round your answers to one decimal place.) X ft from the origin at an angle of 5.7 X from the eastern direction toward the south. 80.4 With what speed does the ball hit the ground? (Round your answer to one decimal place.) 61.3 X ft/s Submit Answer

Influenced by the gravitational pull of a distant star, the velocity of an asteroid changes from from +20.7 km/s to −19.1 km/s over a period of 2.19 years. (a) What is the total change in the asteroid's velocity? (Indicate the direction with the sign of your answer.)   (b) What is the asteroid's average acceleration during this interval? (Indicate the direction with the sign of your answer.)

Identify the letter that contains two scalars and one vector quantity. choices: distance acceleration velocity    speed mass acceleration    distance weight force    speed weight acceleration   No Answer

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 20 ft/s. 90 ft (a) At what rate is his distance from second base decreasing when he is halfway to first base? (Round your answer to one decimal place.) ft/s (b) At what rate is his distance from third base increasing at the same moment? (Round your answer to one decimal place.) ft/s Need Help? Read It

Determine a unit vector parallel to the resultant vector of 2i + 9j – 9k lb, – 2i – 6j + 8k lb, and - 2i + 6j + 4k lb. i + V X k) lb R = ( -0.206 0.92 j+ | 0.3