Current Attempt in Progress In the javelin throw at a track-and-field event, the javelin is launched at a speed of 20.0 m/s at an angle of 31.5° above the horizontal. As the javelin travels upward, its velocity points above the horizontal at an angle that decreases as time passes. How much time is required for the angle to be reduced from 31.5° at launch to 18.9 °? Number i eTextbook and Media Hint Save for Later Units + Attempts: 0 of 2
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- A rocket is launched at an angle of 53.0° above the horizontal with an initial speed of 100 m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 30.0 m/s 2. At this time, its engines fail and the rocket proceeds to move as a projectile. Find (a) the maximum altitude reached by the rocket, (b) its total time of flight, and (c) its horizontal range.Consider a projectile launched form ground level at an angle of elevation with an initial velocity . The maximum horizontal range is given by xmax=(v 2/0 sin2θ)/g, where g is the acceleration due to gravity. Here is the problem: If a soccer ball is kicked from ground level with an initial velocity of 28 m/sec, what is the smallest positive angle at which the player should kick the ball to reach a teammate 48m down the field? Assume that the ball reaches the teammate at ground level on the fly. Round to the nearest tenth of a degree.William Tell is said to have shot an apple off his son’s head with an arrow. If the arrow was shot with an initial speed of 50.0 m/s and the boy was 26.0 m away, at what launch angle above the horizontal did Bill aim the arrow? (Assume that the arrow and apple are initially at the same height above the ground. Hint: sin2θ = 2sinθcosθ)
- A projectile is launched with a launch angle of 30° with respect to the horizontal direction and with an initial speed of 26 m/s. How do the vertical and horizontal components of the projectile's velocity vary with time?The initial velocity in the x-direction vx0 is related to the initial speed by vx0 = v0 cos 30°. The constant velocity in the x-direction means that the equation describing the time dependence of x for the particle, with x0 taken as 0, is x = x0 + vx0t = 0 + m/s t. The equation for the vertical coordinate, which is constantly accelerating downward at g = 9.8 m/s2, is y = y0 + vy0t − 1 2 gt2 = m/s t + m/s2 t2.You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v at an angle ? with respect to the horizontal. Let the building be 54.0 m tall, the initial horizontal velocity be 8.60 m/s, and the initial vertical velocity be 12.5 m/s. Choose your coordinates such that the positive y-axis is upward, and the x-axis is to the right, and the origin is at the point where the ball is released. (a) With these choices, find the ball's maximum height above the ground and the time it takes to reach the maximum height. maximum height above ground m time to reach maximum height s (b) Repeat your calculations choosing the origin at the base of the building. maximum height above ground m time to reach maximum height sMiltiadis Tentoglou is the current Olympic gold medalist for the running long jump. In one of Miltiadis’ practices, he insanely attempts to jump five people who are laid out on the ground in single file from head to toe. Each of the five individuals are 1.7 meters in height and when Miltiadis launches off the ground his initial resultant velocity is directed 20 degrees above the horizon and the horizontal component of this resultant velocity is 10 m/s. In executing the jump, Miltiadis’ center of mass drops 0.6 meters vertically from the instant of takeoff to the instant of landing. Calculate Miltiadis’ a) initial and final vertical velocities in m/s, b) initial and final resultant velocity magnitudes in m/s, c) total time in the air in seconds and d) how far he was able to jump horizontally in meters. e) How many centimeters of clearance did Miltiadis have on both sides of the jump when jumping the five individuals (assume the clearance distance is the same on both sides of the…
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