A football player punts the ball at a angle. Without an effect from the wind, the ball would travel horizontally. (a) What is the initial speed of the ball? (b) When the ball is near its maximum height it experiences a brief gust of wind that reduces its horizontal velocity by . What distance does the ball travel horizontally?
(a) Initial speed of the ball is
(b) The total displacement will be meter.
When gravity first exerts force on an item, its initial velocity indicates how fast it travels. The final velocity, on the other hand, is a vector number that measures a moving body's speed and direction after it has reached its maximum acceleration.
The range of the football is 60 m.
The angle of the football is released at the angle 45 degree.
The gravitational acceleration is -9.8 m/s2
The initial velocity we have to calculate.
The velocity in the x frame will be constant in all time. Considering the initial velocity
The initial velocity will be positive, that is 24.2 m/s.
The Components of the initial velocity.
The initial velocity in the x frame for part a is .
The velocity in the direction for frame B will beTime is needed for finding the distance
The Y- Components of the initial velocity.
The initial velocity in the y frame for part a is -. As the ball is decreasing so value of velocity became negative.
Putting the value of the given data in the equation
The time is total time 3.49 s, but for going from O to A and then from A to B the time becomes half
The displacement for part A is
The displacement for part A is meter
The displacement for part B is
The displacement for part is meter.
The total displacement will be meter.
Construct Your Own Problem Consider an airplane headed for a runway in a cross wind. Construct a problem in which you calculate the angle the airplane must fly relative to the air mass in order to have a velocity parallel to the runway. Among the things to consider are the direction of the runway, the wind speed and direction (its velocity) and the speed of the plane relative to the air mass. Also calculate the speed of the airplane relative to the ground. Discuss any last minute maneuvers the pilot might have to perform in order for the plane to land with its wheels pointing straight down the runway.
An athlete crosses a -m-wide river by swimming perpendicular to the water current at a speed of m/s relative to the water. He reaches the opposite side at a distance m downstream from his starting point. How fast is the water in the river flowing with respect to the ground? What is the speed of the swimmer with respect to a friend at rest on the ground?
Answer the following questions for projectile motion on level ground assuming negligible air resistance (the initial angle being neither \(0^\circ \) nor \(90^\circ \)):
(a) Is the velocity ever zero?
(b) When is the velocity a minimum? A maximum?
(c) Can the velocity ever be the same as the initial velocity at a time other than at \(t = 0\)?
(d) Can the speed ever be the same as the initial speed at a time other than at \(t = 0\)?
For a fixed initial speed, the range of a projectile is determined by the angle at which it is fired. For all but the maximum, there are two angles that give the same range. Considering factors that might affect the ability of an archer to hit a target, such as wind, explain why the smaller angle (closer to the horizontal) is preferable. When would it be necessary for the archer to use the larger angle? Why does the punter in a football game use the higher trajectory?
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