A football kicker can give the ball an initial speed of 25.0 m/s. What are the (a) least and (b) greatest elevation angles at which he can kick the ball to score a field goal from a point 50.0 m in front of goalposts whose horizontal bar is 3.44 m above the ground? When doing this, you may want to research some trig identities to get a formula involving only tangent functions. Also, since there are two values of angle that will work, maybe the quadratic formula is involved.

A clif with an angled summit 900 m above the valley foor is a popular jumping of point for base jumpers.One particular base jumper gets a running start and runs of the side of the clif with a velocity of 4.00 m/sat an angle that is 25.0◦ below the horizontal, as shown.(a) How long is the base jumper in the air before she opens her parachute 150 m above the valley foor?(b) How far (horizontally) is she away from the clif?

From the window of a building, a ball is tossed from a height yo above the ground with an initial velocity of 7.50 m/s and angle of 21.0° below the horizontal. It strikes the ground 6.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: yo: Assume SI units. Do not substitute numerical values; use variables only.) X; = Y = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. Vi, x Vi, y = m/s %3D %3D m/s (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: yo and t. Assume SI units.)

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 0 with respect to the horizontal. Let the building be 54.0 m tall, the initial horizontal velocity be 9.10 m/s, and the initial vertical velocity be 10.5 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 time to reach maximum height (b) Repeat your calculations choosing the origin at the base of the building. maximum height above ground time to reach maximum height

This problem will involve deriving a formula or two for a projectile launched from one height and angle and landing at a different height on Earth. Begin with a projectile launched at angle 0 above horizontal from a height y₁ with initial velocity Vo. The projectile lands at a point with height y₂. These are the given quantities: vo, 0, y₁, y2 and g. Construct formulae for each of the following, as. a function of given quantities the horizontal distance traveled. the maximum height reached. the time taken. the angle of impact. (find the final velocity components first).

Determine the vector magnitudes and directions for the relative velocities VA/B and VB/A, given these magnitudes and directions for the vectors VA and VB:(a) VA: magnitude 70km/h ; direction 30°VB: magnitude 50km/h ; direction 125°   (b)VA: magnitude 70km/h ; direction 30°VB: magnitude 50km/h ; direction 225° (c) VA: magnitude 70km/h ; direction 30°VB: magnitude 50km/h ; direction 340° (d)VA: magnitude 70km/h ; direction 135°VB: magnitude 50km/h ; direction 60°NOTE: The direction is the angle (degrees) from the positive horizontal axes in an anticlockwise direction.

A Motorcycle Jump. You are planning to make a jump with your motorcycle by driving over a ramp that will launch you at an angle of 30.0° with respect to the horizontal. The front edge of the ramp on which you are supposed to land, however, is 25.0 ft lower than the edge of the launch ramp (ie., your launch height). (a) Assuming a launch speed of 65.0 mph, at what horizontal distance from your launch point should the landing ramp be placed? (b) In order to land smoothly, the angle of the landing ramp should match the direction of your velocity vector when you touch down. What should be the angle of the landing ramp? (a) Number (b) Number Units Units

If the cannon is on ground level, (delta y = 0), how far downrange will the projectile land? vi = 19 m/s, degree 45 (above the horizontal, pointing upward) What is the vi x = ? , what is the vi y = ?

A toy cannon is located 15.0 m horizontally away from the base of a 10.5 m high building. A ball is fired from the cannon at an angle of 60.0°, and it passes some unknown distance above the top edge of the building, 1.5 s after it is being fired. (a) What should be the initial velocity of the ball so that it clears the building?(b) How far above the edge of the building is the ball when it passes over the top edge of the building?(c) Is the ball going down or still going up, at the point where it clears the wall?Justify your answer.(d) If the launch point is at the origin, what the x, y coordinates of the location at which the ball strikes the roof of the building?

A cliff with an angled summit 900 m above the valley floor is a popular jumping off point for base jumpers.One particular base jumper gets a running start and runs off the side of the cliff with a velocity of 4.00 m/sat an angle that is 25.0 degrees below the horizontal, as shown.(a) How long is the base jumper in the air before she opens her parachute 150 m above the valley floor?(b) How far (horizontally) is she away from the cliff?