Concept explainers
The time at which the packet fell off the back ramp.
Explanation of Solution
Given: The speed of the airplane is
The angle is
The distance is
Formula used: Draw the diagram for the representation of the package when it fell off the ramp.
Write the expression for the distance in x direction.
Here,
Write the expression for the distance in y direction.
Here,
Write the expression for the x coordinate along the parabolic trajectory of the airplane.
Here,
Write the expression for the y coordinate along the parabolic trajectory of the airplane.
Here,
Substitute
Substitute
Simplify the above equation
Write the expression for the velocity component with respect to x axis.
Here,
Write the expression for the velocity component with respect to y axis.
At impact, the horizontal distance is
Write the expression for the distance to impact.
Simplify the above equation for
Substitute
Substitute
Solve the above equation using binomial expansion.
Calculation:
Substitute
Substitute
Substitute
Conclusion:
Thus, the time at which the packet fell off the back ramp is
Want to see more full solutions like this?
Chapter 3 Solutions
Physics For Scientists And Engineers Student Solutions Manual, Vol. 1
- A man on a motorcycle traveling at a uniform speed of 10 m/s throws an empty can straight upward relative to himself with an initial speed of 3.0 m/s. Find the equation of the trajectory as seen by a police officer on the side of the road. Assume the initial position of the can is the point where it is thrown. Ignore air resistance.arrow_forwardA particle initially located at the origin has an acceleration of a=3.00jm/s2 and an initial velocity of vi=5.00im/s. Find (a) the vector position of the particle at any time t, (b) the velocity of the particle at any time t, (c) the coordinates of the particle at t = 2.00 s, and (d) the speed of the particle at t = 2.00 s.arrow_forwardA motorist drives south at 20.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.00 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.00-min trip, find (a) the total vector displacement, (b) the average speed, and (c) the average velocity. Let the positive x axis point east.arrow_forward
- Suppose a soccer player kicks the ball from a distance 24 m toward the goal. Find the initial speed of the ball if it just passes over the goal, 2.4 m above the ground, given the initial direction to be 41° above the horizontal. Answer = ??? m/sarrow_forwardIf a particle moves such that y=x2 , and the x velocity is a non-zero constant v=b, if the initial y-velocity is zero, find the time (in terms of b) when the angle of the velocity is 26.56 degrees above the horizontal.arrow_forwardAn airplane in a holding pattern flies at constant altitude alonga circular path of radius 3.50 km. If the airplane rounds half thecircle in 1.50 x 102 s, determine the magnitude of its (a) displacementand (b) average velocity during that time. (c) Whatis the airplane’s average speed during the same time interval?arrow_forward
- Pan am Flight 7 was one of the famous planes to disappear into the Bermuda Triangle, which is en route from San Francisco to Hawaii . The first route is due west for 602 km; then it took a detour southeast for 705 m; and the its final route is at 53° north of west, the crash site in the Pacific ocean, for 636 km. What is the plane’s total displacement? Add solution.arrow_forwardA student drives 10 km to the north and then 20 km 30° S of E. By using the component method, what are the magnitude and direction of his displacement from the starting point?arrow_forwardWhen a ball was allowed to fall from rest from height h, a second ball was thrown up from the ground in the vertical direction. For two balls to meet at height h / 2, what should be the initial velocity of the second ball?arrow_forward
- The positionr→of a particle moving in an xy plane is given byr→=(5.00t3−6.00t)i^+(2.00−2.00t4)j^withr→in meters and t in seconds. In unit-vector notation, calculate(a)r→, (b)v→, and (c)a→for t = 2.00 s. (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? Give your answer in the range of (-180o; 180o).arrow_forwardQuestion 2: #63 In 1780, in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running horizontally off the edge of the cliff above Ohio's Cuyahoga River, which is con-fined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ft across while falling 20 ft. Tall tale, or possible? a. What is the minimum speed with which he'd need to run off the edge of the cliff to make it safely to the far side of the river? b. The world-record time for the 100 m dash is approximately 10 s. Given this, is it reasonable to expect Brady to be able to run fast enough to achieve Brady's leap?arrow_forwardA field biologist is studying the migration patterns of northern gannets (a type of seabird). On one particular day, she records that they fly 5.0 km northeast, then turn toward to the south of east by 30◦ and fly 4.0 km in the new direction. How far east of their original position are the birds?arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning