A diwali rocket, when ignited at the ground level, rises vertically upwards to the level of a window 10 m from ground. Find the magnitude of velocity of the rocket at the time of its projection.

Consider a projectile launched at a height h feet above the ground and at an angle ? with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modeled by the parametric equations x = t(v0 cos(?)) and y = h + (v0 sin ?)t - 16t2.Let h=6, v0=63.25, and ?=0.79.  What is the range of the projectile (i.e., how far does it travel? Round your answers to two decimal places).

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

A tennis ball is projected at ground level. After 2 seconds, it just clears a net 2.5 metres high at a horizontal distance of 30 metres. Find:i) The angle of projection and the initial velocity ii) The time of flight and the range

From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 9.00 m/s and angle of 21.0° below the horizontal. It strikes the ground 4.00 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: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi =       yi =       (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. vi, x =  m/s vi, y =  m/s (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x =        m y =        m (d) How far horizontally from the base of the building does the ball strike the ground? m(e) Find the height from which the ball was thrown. m(f) How…

From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.60 m/s and angle of 18.0° below the horizontal. It strikes the ground 5.00 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: y0.) xi =       yi =       (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. vi,x =  m/s vi,y =  m/s (c) Find the equations for the x- and y- components of the position as functions of time. (Use the following as necessary: y0 and t. Let the variable t be measured in seconds.) x =        m y =        m (d) How far horizontally from the base of the building does the ball strike the ground? m(e) Find the height from which the ball was thrown. m(f) How long does it take the ball to reach a point 10.0 m…

From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.70 m/s and angle of 21.0° below the horizontal. It strikes the ground 4.00 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: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi =     yi =     (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. vi, x = m/s vi, y = m/s (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x =     m y =     m (d) How far horizontally from the base of the building does the ball strike the ground? m (e) Find the height from which the ball was thrown. m (f) How long does…

A baseball player hits a home run, and the ball lands in the left-field seats, y = 7.70 m above the point at which it was hit. It lands with a velocity of v = 35.0 m/s at an angle of 28° below the horizontal (see the Figure). The positive directions are upward and to the right in the drawing. Ignorin air resistance, find (a) the magnitude and (b) the direction of the initial velocity with which the ball leaves the bat. +y voy 28° y=7.70m VOI v 35.0m/s

The position r of a particle moving in an xy plane is given by ř seconds. In unit-vector notation, calculate (a) 7, (b) V , and (c) a for t = 3.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 3.00 s? Give your answer in the range of (-180°; 180°). (4.00r3 – 1.00t)î + (5.00 – 1.00r4)j with 7 in meters and t in (a) Number i i Units (b) Number ît i Units i (c) Number i i Units (d) Number i Units

A river of width' a'with straight parallel banks flows due north with speed u. The points O and A are on opposite banks and A is due east of O. Coordinate axes Ox and Oy are taken in the east and north directions respectively. A boat, whose speed is v relative to water, starts from O and crosses the river. If the boat is steered due east and u varies with x as : u = x(a – x)- Find : absolute velocity of boatman when he reaches the opposite bank