- Learning Goal To Understand Projectile Motion By Considering Horizontal Constant Velocity Motion And Vertical Constant 1 (108.05 KiB) Viewed 100 times
Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth's gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: 1. An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, , is constant. < 1 of 2 > ↑ peak height y, or Упах Vo to ol initial position (xo yo) Figure 0₁ 1₁ X₁ 1₂ Distance Downrange range x₂ or R Review | Constant Part C What are the values of the velocity vector components ₁,2 and 1, (both in m/s) as well as the acceleration vector components a1, and @1, (both in m/s²)? Here the subscript 1 means that these are all at time t₁- O 0, 0, 0, 0 O 0, 0, 0, -9.80 O 15.0, 0, 0, 0 Screenshot O 15.0, 0, 0, -9.80 O 0, 26.0, 0, 0 O 0, 26.0, 0, -9.80 O 15.0, 26.0, 0, 0 O 15.0, 26.0, 0, -9.80 Submit Request Answer The flight time refers to the total amount of time the ball is in the air, from just after it is launched (tu) until just before it lands (t₂). Hence the flight time can be calculated as t₂- tŋ, or just t₂ in this particular situation since t = 0. Because the ball lands at the same height from which it was launched, by symmetry it spends half its flight time traveling up to the peak and the other half traveling back down. The flight time is determined by the initial vertical component of the velocity and by the acceleration. The flight time does not depend on whether the object is moving horizontally while it is in the air. Part D If a second ball were dropped from rest from height ymax, how long would it take to reach the ground? Ignore air resistance.
Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth's gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: 1. An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, Ux. is constant. 1 of 2 > ↑ peak height y₁ or ymax /to O initial position (xo-yo) Figure U₁ 1₁ X₁ 1₂ Distance Downrange range x₂ or R Part D If a second ball were dropped from rest from height ymax, how long would it take to reach the ground? Ignore air resistance. Check all that apply. ► View Available Hint(s) to Otto Screenshot Ot₂ ty-h t-to 2 Submit 2 The range R of the ball refers to how far it moves horizontally, from just after it is launched until just before it lands. Range is defined as 2-0, or just ₂ in this particular situation since x = 0. Range can be calculated as the product of the flight time to and the x component of the velocity ₂ (which is the same at all times, so 1) = 0). The value of V, can be found from the launch speed and the launch angle using trigonometric functions, as was done in Part B. The flight time is related to the initial y component of the velocity, which may also be found from and using trig functions. The following equations may be useful in solving projectile motion problems, but these equations apply only to a projectile launched over level ground from position (20 = 3/0 = 0) at time to =0 with initial speed and launch angle measured from the horizontal. As was the case above, t refers to the flight time and R. refers to the range of the projectile. 2v sin(0) flight time: t₂ = 200 9 9 ▼ =
Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth's gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: 1. An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, is constant. 1 of 2 > peak height. y₁ or ymax Vo /10 to of initial position (xo-yo) Figure V₁ -1₁ X₁ 21 Distance Downrange ₂ range x₂ or R Review | Constant component of the velocity, which may also be found from and using trig functions. The following equations may be useful in solving projectile motion problems, but these equations apply only to a projectile launched over level ground from position (20 = 3/0 = 0) at time to =0 with initial speed and launch angle measured from the horizontal. As was the case above, to refers to the flight time and R refers to the range of the projectile. 200x flight time: £2 = = 22 sin(0) y 9 sin(20) range: R = V₂t₂ = 9 In general, a high launch angle yields a long flight time but a small horizontal speed and hence little range. A low launch angle gives a larger horizontal speed, but less flight time in which to accumulate range. The launch angle that achieves the maximum range for projectile motion over level ground is 45 degrees. Screenshot Part E Which of the following changes would increase the range of the ball shown in the original figure? Check all that apply. Increase v above 30 m/s. Reduce below 30 m/s. Reduce from 60 degrees to 45 degrees. Reduce from 60 degrees to less than 30 degrees. Increase from 60 degrees up toward 90 degrees. Submit Request Answer Provide Feedback Next >