A student throws a water balloon with speed v0 from a height h = 1.82 m at an angle θ = 33° above the horizontal toward a target on the ground. The target is located a horizontal distance d = 6.5 m from the student’s feet. Assume that the balloon moves without air resistance. Use a Cartesian coordinate system with the origin at the balloon's initial position. Part (a)  What is the position vector, Rtarget, that originates from the balloon's original position and terminates at the target? Put this in terms of h and d, and represent it as a vector using i and j. Part (b)  In terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. Your answer should not include h.  Part (c)  Create an expression for the balloon’s vertical position as a function of time, y(t), in terms of t, vo, g, and θ.

In my homework, I am asked to derive an equation for V0.   The homework question is as follows: A howitzer fires a shell with a velocity of v0 at an angle Θ above the horizontal. The howitzer is on a plateau and the shell lands down in the plain below, a vertical distance d below the plateau and a horizontal distance L from where the howitzer is. Derive an expression for the magnitude of the initial velocity, V0, as a function of d, L, g, and Θ.   Any help would be appreciated as I have worked on this problem for quite a while and I am not making progress.

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…

In the figure, a ball is thrown leftward from the left edge of the roof, at height h above the ground. The ball hits the ground 1.50 s later, at distance d = 26.0 m from the building and at angle e = 62.0° with the horizontal. (a) Find h. (Hint: One way is to reverse the motion, as if on videotape.) What are the (b) magnitude and (c) angle relative to the horizontal of the velocity at which the ball is thrown (positive angle for above horizontal, negative for below)? (a) Number Units (b) Number Units (c) Number Units

For an interesting physics field trip, we visit Tahquamenon Falls in the Upper Peninsula. We measure the horizontal speed of the water at the top of the falls to be 3.00 m/s. How far vertically below the top edge of the falls does the velocity vector of the water point downward at a 59.3 degrees angle below the horizontal?

A car is moving on a straight road in a fixed direction at a constant speed of v = 64 km/h with respect to the road. You wish to state the kinematic vectors of the motion of the car by using a Cartesian coordinate system whose positive x-axis is pointed in the direction of the motion of the car and the origin is fixed at some point on the road. Part (a) What is the expression for the velocity of the car, using the speed v and the unit vectors i, j, and k? Part (b) What is the x-component of the position vector, in units of kilometers, at time t = 0.035 hr?

A turtle ambles leisurely from a location with position vector r1,x = 1.87 m and ri.y = -2.95 m in a lettuce garden to another location with position vector r2.x = 3.91 m and r2.y = -4.27 m, where the lettuce appears to be tastier. The excursion takes 5.17 min to complete. What are the components and the magnitude of the turtle's average velocity in meters per second? Vav,x m/s Vav,y m/s %3D m/s %3D

Problem 3:   Consider a projectile launched with an initially horizontal velocity of 19.7m from a cliff of height h=9.23m. It travels a horizontal distance, d, before striking the ground at an angle θ below the horizontal. Use the Cartesian coordinate system provided in the drawing with the origin at the base of the cliff. Assume that air resistance is negligible.    Part (a)  How much time elapses, in seconds, from the moment the projectile is launched until it strikes the ground?   Part (b)  What is the horizontal distance, in meters, traveled by the projectile?  Part (c)  What is the speed of the projectile, in meters per second, as it strikes the ground? Part (d)  What is the impact angle, in degrees below the horizontal, at which the projectile strikes the ground?