A projectile is fired with a velocity u at the entrance A to a horizontal tunnel of length L and height H. Determine the minimum value of u and the corre- sponding value of the angle 6 for which the projectile will reach B at the other end of the tunnel without touching the top of the tunnel. H A
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- 8. You fire a ball with an initial speed of v at an angle o above the surface of an incline, which is itself inclined at an angle 0 above the horizontal. a) Find the distance, measured along the incline, from the launch point to the point when the ball strikes the incline. b) What angle o gives the maximum range, measured along the incline? Ignore air resistance.Just need Dab 3. Three projectiles (A, B, and C) are launched with different initial speeds so that they reach the same maximum height, as shown in the figure. List the projectiles in order of increasing initial speed (smallest v; written in the first blank). у then
- During a baseball game, a baseball is struck at ground level by a batter. The ball leaves the baseball bat with an initial speed v0 = 42 m/s at an angle θ = 43° above horizontal. Let the origin of the Cartesian coordinate system be the ball's position the instant it leaves the bat. Air resistance may be ignored throughout this problem. a.)Express the magnitude of the ball’s initial horizontal velocity v0x in terms of v0 and θ. b.)Express the magnitude of the ball’s initial vertical velocity v0y in terms of v0 and θ. c.)Find the ball’s maximum vertical height hmax in meters above the ground.A baseball is hit with an initial velocity of 20 m/s at an angle of 22 degrees above the horizontal and at an initial height of .9 m. a. How high will the baseball go? b. How far will the baseball go when it hits the ground?Problem 4 Derive expressions for the velocity (7) and acceleration (a) vectors in spherical coordinates. That is, transform and a from the Cartesian system of (x, y, z) to (r, 0, 0).
- A secret agent skis off a slope inclined at θ = 28.3 degrees below horizontal at a speed of v0 = 17.4 m/s. He must clear a gorge, and the slope on the other side of the gorge is h = 11.9 m below the edge of the upper slope. a.)What is the maximum width, w, of the gorge (in meters) so that the agent clears it?A high diver leaves the end of a 5.5 mm high diving board and strikes the water 1.2 ss later, 3.5 mm beyond the end of the board. Considering the diver as a particle, Part C Determine the maximum height reached. Express your answer to two significant figures and include the appropriate units. Part D Determine the magnitude of the velocity v⃗fwith which she enters the water. Express your answer to two significant figures and include the appropriate units. Part E Determine the angle of the velocity v⃗f with which she enters the water. Express your answer to two significant figures and include the appropriate units.I throw a ball to my dog at h = 1.8 m above the ground, with initial velocity v0 = 10.25 m/s at an angle θ = 31° above horizontal. Assume the ballencounters no air resistance, and use a Cartesian coordinate system with the origin located at the ball's initial position.a. My dog jumps up in the air and catches the ball at the same height that Ithrew it. Create an expression for the time, tf, the ball is in the air in terms of v0, θ, g, and h. b. Calculate the horizontal distance, d in meters, between me and my dog
- Danielle launches a ball off of a platform of height h with velocity vo at an angle 0 above the horizontal. A wall with a ball-sized hole a height H above the floor, with H > h, is a horizontal distance L = 24.0 m away from Danielle. The difference in height between H and h is one-twelfth of L, and the square of the magnitude of the velocity, v, is three-halves of the product gL. H 1 H – h = h 3 L Determine the two values of 0 that ensure the ball passes through the hole. Submit the larger angle as 0, and the smaller angle as 02.A person swings from a trapeze, projects herself at angle of 53 degrees, and is supposed to be caught by person B, whose hands are 6.1m above and 8.2m horizontally from persob A's launch point. a. What initial speed must Person A have just to reach person B? b. If person B misses person A completely as she flies past, how far horizontally does person A travel, from her initial launch point, before landing in the safety net 8.6m below her starting point? PROVIDE ILLISTRATION8. You fire a ball with an initial speed of v at an angle o above the surface of an incline, which is itself inclined at an angle e above the horizontal. a) Find the distance, measured along the incline, from the launch point to the point when the ball strikes the incline. b) What angle o gives the maximum range, measured along the incline? Ignore air resistance.