2. A soccer ball is kicked into the air so that the path of its flight can be modeled by the function, where t is in seconds and x is meters above ground: X(t) = –4.9t² +9.8t + 5 a) At what time will the ball land? b) How many meters above ground was the ball kicked? c) What is the maximum height the ball will reach and at what time will this occur? d) What is the acceleration (with direction) of the ball at t=3 s?

2. A soccer ball is kicked into the air so that the path of its flight can be modeled by the function, where t is in seconds and x is meters above ground: X(t) = –4.9t² +9.8t + 5 a) At what time will the ball land? b) How many meters above ground was the ball kicked? c) What is the maximum height the ball will reach and at what time will this occur? d) What is the acceleration (with direction) of the ball at t=3 s?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 58AP: A football receiver running straight downfield at 5.50 m/s is 10.0 m in front of the quarterback...

See similar textbooks

Similar questions

A football receiver running straight downfield at 5.50 m/s is 10.0 m in front of the quarterback when a pass is thrown downfield at 25.0 above the horizon (Fig. P3.58). If the receiver never changes speed and the ball is caught at the same height from which it was thrown, find (a) the footballs initial speed, (b) the amount of time the football spends in the air, and (c) the distance between the quarterback and the receiver when the catch is made. Figure P3.58
A projectile is launched from the point (x = 0, y = 0), with velocity (12.0i19.0j)m/s2, at t = 0. (a) Make a table listing the projectiles distance r from the origin at the end of each second thereafter, for 0 t 10 s. Tabulating the x and y coordinates and the components of velocity vx and vy will also be useful. (b) Notice that the projectiles distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the velocity. Suggestion: Argue that if v is not perpendicular to r, then r must lie increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain your method for solving part (c).
Unreasonable Results A commercial airplane has an air speed of 280 m/s due east and flies with a strong tailwind. It travels 3000 km in a direction 5° south of east in 1.50 h. (a) What was the velocity of the plane relative to the ground? (b) Calculate the magnitude and direction of the tailwind's velocity. (c) What is unreasonable about both of these velocities? (d) Which premise is unreasonable?
A daring ranch hand sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 10.0 m/s, and the distance from the limb to the level of the saddle is 3.00 m. (a) What must be the horizontal distance between the saddle and limb when the ranch hand makes his move? (b) For what time interval is he in the air?
Galileo thought about whether acceleration should be defined as the rate of change of velocity over time or as the rate of change in velocity over distance. He chose the former, so lets use the name vroomosity for the rate of change of velocity over distance. For motion of a particle on a straight line with constant acceleration, the equation v = vi + at gives its velocity v as a function of time. Similarly, for a particles linear motion with constant vroomosity k, the equation v = vi + kx gives the velocity as a function of the position x if the particles speed is vi at x = 0. (a) Find the law describing the total force acting on this object of mass m. Describe an example of such a motion or explain why it is unrealistic for (b) the possibility of k positive and (c) the possibility of k negative.
An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration clue to gravity have the same sign on the way up as on the way clown?
Two students are on a balcony a distance h above the street. One student throws a ball vertically downward at a speed vi, at the same time, the other student throws a ball vertically upward at the same speed. Answer the following symbolically in terms of vi, g, h. and t. (a) What is the time interval between when the first ball strikes the ground and the second ball strikes the ground? (b) Find the velocity of each ball as it strikes the ground, (c) How far apart are the balls at a time t after they are thrown and before they strike the ground?
(a) By taking the slope of the curve in Figure 2.60, verify that the velocity of the jet car is 115 m/sat t=20 S. (b) By taking the slope of the curve at any point in Figure 2.61, verify that the jet car's acceleration is 5.0 m/s2.
2) A ball is thrown from a height of 1 metre on the Moon with an initial (upwards) verticalcomponent of velocity of 10 metres per second. You may assume that the accelerationdue to gravity on the Moon is gmoon = 1.62 metres per second per second.(a) How long does the ball take to reach the ground? (b) The ball hits the ground at a horizontal distance of 150 metres from where it wasthrown. What was the magnitude of the horizontal component of its velocity?
3. A building is 46.0 m tall. A jealous boyfriend wishes to drop a tomato from the top of the building onto the head of his girlfriend’s suitor, who is 1.80 m and walking alongside the building at a constant speed of 1.20 m/s. How many meters should the suitor be from the position below the tomato when it is dropped? With complete solution
A certain volcano on Earth can eject rocks vertically to a maximum height H. (a) How high (in terms of H) would these rocks go if a volcano on Mars ejected them with the same initial velocity? The acceleration due to gravity on Mars is 3.71 m/s2. (Ignore air resistance on both planets.) (b) The rocks are in the air for a time T on Earth, How long (in terms of T) would they be in the air on Mars?
1. A stone is dropped from the top of a tower 40m height. At the same time another stone is thrown upward from the foot of the tower with an initial velocity of 20m/s. At what distance from the top and after how much time the two stones cross each other If it takes 2.6 seconds in falling on the ground, find the height of the building.