Classical Mechanics Answers

3. A new game has been invented where the player has to combine a dive from a board with shooting of a basketball through a hoop (see figure below). As a student of PHY 101 you decide to take part in this game. During your practice sessions, you realize that while standing on the diving board 4.50 m above the water, you are able to score into the hoop which is a horizontal distance of 6.50 m away from the board and 1.00 m above ground level. (a) With what speed did you launch the basketball? (b) Now you step off the diving board and launch the ball in order to make a basket into a hoop that is a horizontal of 3.75 m, at what time after stepping off the board should you launch the ball? (c) What are the horizontal and vertical components of the ball’s velocity at the instant of launch?

On a beautiful day you decide to go fishing with your younger brother Ben. Ben has not been fishing before so he doesn't know how to properly cast out his line. He puts the lure 15.0 cm above the water before letting it drop straight down. The line accelerates until it hits the water then continues to the bottom of the lake at a constant speed. It takes the lure 7.50 s to reach the bottom of the lake from when it was released by Ben.

How deep is the lake? (Assume the lure accelerates at the free fall rate of 9.8 m/s2 until it hits the water.)

As two boats approach the marina, the velocity of boat 1 relative to boat 2 is 2.15 m/s in a direction 47.0° east of north. If boat 1 has a velocity that is 0.775 m/s due north, what is the velocity (magnitude and direction) of boat 2?

In a soccer game a midfielder kicks the ball from one touchline directly toward the other with a velocity of 14.0 m/s (along the positive x-axis). After the ball travels for 2.50 s, a striker makes an acrobatic kick that gives the ball a new velocity in the y direction, and after 0.900 s the ball passes the diving goalkeeper and goes into the net. If the total displacement of the ball is 40.2 m at 29.5° above the x positive axis, with what speed did the striker kick the ball?

A 2kg yellow cart rolls right with velocity of 6 m/s and collides with a 3kg orange cart moving right with velocity of 1 m/s. After collision, the orange cart moves right with velocity of 5 m/s. What is speed and direction of of the yellow cart?

2. Two marbles are launched at t = 0 in the experiment illustrated in the figure below. Marble 1 is launched horizontally with a speed of 4.20 m/s from a height h = 0.950 m. Marble 2 is launched from ground level with a speed of 5.94 m/s at an angle above the horizontal. (a) Where would the marbles collide in the absence of gravity? Give the x and y coordinates of the collision point. (b) Where do the marbles collide given that gravity produces a downward acceleration of g = 9.81 m/s2? Give the x and y coordinates.

A body of mass 2.60 kg is pushed straight upward by a 31.2 N vertical force. What is it’s acceleration?

(a) You and your new alien friend, Howard need to escape area 51 fast! Luckily, Howard knows of a high-end sports car you can use in your escape. Assuming you don't get shot in the process, what is the minimum acceleration necessary to reach a linear displacement of 5.00 km in under 2.00 minutes? Assume you start from rest and maintain a constant acceleration. (b) Howard's Bugatti has a maximum acceleration around 11.0 m/s2 and a top speed of about 260.0 mph. What is the least amount of time it will take you to reach a linear displacement of 5.00 km if you accelerate at a constant rate of 11.0 m/s until reaching top speed and then cruise at the top speed for the remainder of the trip into Mexico? (

A particle is moving in x-y plane. It's initial velocity & acceleration are u=(4î+5ĵ) m/s and a=(2î-4ĵ) m/s^2. Find
(1) the time when the particle will cross the x axis
(2) x coordinate of the particle at that instant
(3) velocity of the particle at this instant
Initial coordinates of particle are (4m,10m)

high fountain of water is located at the center of a circular pool not wishing to get his wet a student walk around the pool and measure its circumference to be 15.0 m. next the student at the edge of the pool and uses a protector to gauge the angle of alivation of the top of the mountain be 55.0 degree.How high is the fountain?