Concept explainers
Projectile trajectories A projectile (such as a baseball or a cannonball) launched from the origin with an initial horizontal velocity u0 and an initial vertical velocity v0 moves in a parabolic trajectory given by
where air resistance is neglected and g ≈ 9.8 m/s2 is the acceleration due to gravity (see Section 11.7).
- a. Let u0 = 20 m/s and v0 = 25 m/s. Assuming the projectile is launched over horizontal ground, at what time does it return to Earth?
- b. Find the integral that gives the length of the trajectory from launch to landing.
- c. Evaluate the integral in part (b) by first making the change of variables u = −gt + v0. The resulting integral is evaluated either by making a second change of variables or by using a calculator. What is the length of the trajectory?
- d. How far does the projectile land from its launch site?
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Chapter 11 Solutions
CODE/CALC ET 3-HOLE
Additional Engineering Textbook Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Precalculus (10th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
- The spring in the figure below is stretched from its equilibrium position at x = 0 to a positive coordinate xo. ko HINT x = 0 x = xo PE sn PE 50 The force on the spring is F and it stores elastic potential energy PESO. If the spring displacement is tripled to 3x, determine the ratio of the new force to the original force, and the ratio of the new to the original elastic potential energy, Fo Fo PESO (a) the ratio of the new force to the original force, PE ST PE SO (b) the ratio of the new to the original elastic potential energy,arrow_forwardTwo small charged objects attract each other with a force F when separated by a distance d.If the charge on each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2,the force becomes?arrow_forward3. The velocity of a particle which starts from rest is given by the following table. t see) 0 2 8 10 12 14 16 v (fusee) o 12| 16 26 40| 44 25 12 18 Evaluate using trapezium rule, the total distance travelled in 18 seconds.arrow_forward
- Example 7: Rocket sleds were used to test aircraft and its effects on human subjects at high speeds. It is consisted of four rockets; each rocket creates an identical thrust T. Calculate the magnitude of force exerted by each rocket (T) for the four-rocket propulsion system shown in the Figure. The sled's initial acceleration is 49 m/s, the mass of the system is 2100 kg, and the force of friction opposing the motion is known to be 650 N. Solution: H.W Free-body diagramarrow_forwardA simple pendulum of length L, has a maximum angular displacement e_max. At one point in its motion, its kinetic energy is K = 3 J and its potential energy is U = 4.2 J. When the pendulum's angular velocity is one-fourth its maximum value (0' = %3D O'_max/4), then its kinetic energy is:arrow_forward1, t>0 10, t<0 Let u(t) The total energy E of the function x(t) = sin(3t)u(t), is O Eo = 0 O E = 00 O Ex = 0.5 O E = 0.25arrow_forward
- Q1/The pressure drop in pascals (Pa) for a fluid flowing in a pipe with a sudden decrease in diameter can be determined based on the loss of head equation given below: h = 24-11 2g Area A Area A Area A Where: V₂ is the velocity in position 2 (m/s), g: is acceleration due to gravity = 9.81 m/s², A₁ and A₂ are the cross-sectional areas of the tube in position 1 and 2 respectively. A==d² Where: d is the diameter (m). Write a program in a script file that calculates the head loss. When the script file is executed, it requests the user to input the velocity (V₂) in m/s and values of diameters (d, and d₂). The program displays the inputted value of v followed by a table with the values of diameters in the first and second columns and the corresponding values of h, in the third column. 2 2arrow_forward2. The position of an object moving along the z-axis is described by *(t) = 21²-t +4, where the position, z, is in m and the time, t, is in s. Find: a. the average velocity between t = 1 8 and ty= 3 s. b. the velocity at t = 2 s. b. the acceleration at t = 4 s.arrow_forwardLet a be the angle between the vectors u=(3.0.4) and v-(4.0.3). Then* O None of these O sin(a)= 24/25 cos(a)= 24/25 cos(a)= - 24/25arrow_forward
- In matlab We have two vectors containing the weight and height of a group of people. The vector H contains the measurement data of height (in meters) H=[1.92 1.58 1.69 2.10 1.96 1.81 1.59 1.91 1.61 1.71 1.68 1.54 1.93 2.14 1.83 1.71 1.82 1.88 1.74 1.65 1.59 1.60 1.66 1.78 1.81] the vector V contains the measurements of weight in kilograms V= [116.4 52.7 67.2 51.8 100.8 102 94.3 68.6 92.9 46.3 82.1 89.3 66.6 77.6 137.7 83.8 72.2 77.7 96.9 44.6 57.4 86.6 72.8 58.1 66.7] Use the controllstructures (loops and condition tests), do not use mean() or std() in Matlab. create a script to find the following. a) what is the average height b) what is the standard deviation of the height c) find the BMI (body mass index) for all the subjects, it's going to be a vector with values for all the subjects. d) how many have a normal weight BMI (under 18.5 and over 25)arrow_forward4. Consider the building from the figure below. a) If it is 200 feet tall and you are 20 feet away, at what angle from the ground will you have to tilt your head to see the top of the building? (For simplicity assume that your head is even with the ground.) How far is it from your head to the top of the building? Repeat parts (a) and (b) assuming your head is NOT even with the ground, but is 6 feet above ground level. b) c) angle distance d height harrow_forward(Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.arrow_forward
- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr
![Text book image](https://www.bartleby.com/isbn_cover_images/9781133187844/9781133187844_smallCoverImage.gif)