An object is thrown off the top of a building with velocity 36 m/s at an angle of 23° with respect to the horizontal. The object travels a horizontal distance of 260 m before landing on the ground. (a)  How high is the building in meters?  (b)  What is the magnitude of the velocity of the object when it reaches the ground?  (c)  What is the direction of the object when it reaches the ground, in degrees from the positive x-axis?

use proper vector notations.

A plane flies 493 km east from city A to city B in 45.0 min and then 983 km south from city B to city C in 1.30 h. For the total trip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its average velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east). (a) Number i Units (b) Number Units (c) Number i Units (d) Number i Units (e) Number Units II

Problem 2: An object is thrown off the top of a 38-m tall building with a velocity of 350 m/s at an angle of 8.2° with respect to the horizontal. Part (a) How long is the object in the air in seconds? Numeric : A numeric value is expected and not an expression. t = Part (b) What is the maximum height the object reaches above the ground in meters? Numeric : A numeric value is expected and not an expression. hmax = Part (c) What is the horizontal distance the object covers in meters? Numeric : A numeric value is expected and not an expression. Ax =.

A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10° to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 500 mi/h, how far is she from her starting position? (Round your answer to the nearest mile.)

A placekicker is about to kick a field goal. The ball is 21.7 m from the goalpost. The ball is kicked with an initial velocity of 19.1 m/s at an angle above the ground. Between what two angles, 0₁ and 02, will the ball clear the 2.67-m-high crossbar? Give your answers as (a) the smaller angle and (b) the larger angle. (Hint: The following trigonometric identities may be useful: sec 0 = 1/(cos) and sec²0 = 1 + tan²0.) (a) Number (b) Number Units Units 0₂

A swimmer who can consistently keep the same pace to cover 50 meters in 6.8 seconds sets out to swim across a river. The current in the river moves at 3.2 meters per second as the swimmer keeps a constant pace trying to get directly across (at a right angle to the current).  What is the actual speed of the swimmer compared to land? (Your answer should be in meters per second. Remember to calculate a speed first, then add vectors using Pythagorean Theorem)

A skateboarder shoots off a ramp with a velocity of 7.9 m/s, directed at an angle of 51° above the horizontal. The end of the ramp is 1.4 m above the ground. Let the x axis be parallel to the ground, the +y direction be vertically upward, and take as the origin the point on the ground directly below the top of the ramp. (a) How high above the ground is the highest point that the skateboarder reaches? (b) When the skateboarder reaches the highest point, how far is this point horizontally from the end of the ramp? (a) Number_____  Units_____                                                            (b) Number ____  Units ____

A golf ball is hit upward, with an initial velocity of 47 meters per second, at an angle of 25° with respect to the horizontal. The ball is hit from a height of 8 meters above the ground.   The horizontal distance x from the starting point and the height y above the ground of the ball t seconds after it is hit are given by the parametric equations below.   x=(v0cosθ)t y=−4.9t^2+(v0sinθ)t+h Here v0 is the initial velocity, θ is the initial angle with respect to the horizontal, and h is the initial height.   Use the equations to answer the following questions.   (a)How long is the ball in the air before it first touches the ground?Do not round any intermediate computations. Round your answer to the nearest hundredth. _____ seconds (b)What is the horizontal distance the ball travels before it first touches the ground?Round your answer to the nearest whole number. _____ meters

Calculate the y-component of the acceleration vector a1, which has a magnitude of 26 m/s2 and has an angle below the positive x-axis of 29 degrees.