A fireworks shell P is launched upward from point A and explodes at its apex at an altitude of 260 ft. Relative to an observer at O, determine the values of i and O when the shell reaches an altitude y = 195 ft. Neglect aerodynamic drag.

Consider the process of escaping from the solar system starting from the surface of Earth. Assume there are no other bodies involved. Earth has an orbital speed about the Sun of 29.8 km/s. Hint: 2GM does not apply. Use mv,? GM_m GM m 2 GM-m GMs" which includes the potential energy of both Earth and the Sun. 2.5 V. esc 2,E (a) What minimum speed relative to Earth (in km/s) would be needed? km/s In what direction should you leave Earth? O opposite the direction of Earth's orbital velocity O towards the Sun O away from the Sun O in the direction of Earth's orbital velocity (b) What will be the shape of the trajectory? O a circle O an ellipse O a hyperbola O a parabola

A firework is to be fired at an angle of θ = 75 ∘ and initial speed v = 70 m / s .   A timed fuse will make the firework explode a time T after launch.  What should T be so that the firework explodes at the highest point on the trajectory (the apogee) ?

As seen in the image provided, a double-star system with stars of equal mass rotate in circular orbits around their mutual center of mass that is halfway between them. One of the stars (α) is bright. The other star (β) is its unseen dark companion. Our line of sight passes through the orbital plane such that once in every period, α approaches head-on, and once ever period it recedes directly away. The same is true for β. Suppose light always moves at speed c relative to the source that emits it (i.e., if v is the orbital speed of each star, light travels toward us at speed c + v from α when it is headed toward us, and at speed c - v when it is headed away from us, as depicted). The double-star system is a distance d away from Earth. How long would take light to get to Earth from α if the light is emitted when α is (i) coming toward us, and (ii) moving away from us?

Prove the following equation Pw(x,t)= py(x,t) with p=2 ww in (2x-1) Knowing that y (x,t)= 3e^

Given: R(N)=f(N)g(N) where f(N) = 7.2N and g(N) = (1 - 7.9/N. If R(N) = H means that R'(N) = 0 and H = 10.5N, what is the value of N that causes R'(N) = 0?

The 20-lb block has a speed of 8 ft/s when the force of F = (16t^3) lb is applied. Determine the velocity of the block when t = 2.45sec. The coefficient of kinetic friction at the surface is μk = 0.2.

I. With external gravitational field In this second part you are asked to analyze rocket propulsion with the present of gravitational field g. This appears for instance when the rocket is launching from the surface of a planet. (1) Describes why you are not allowed to use the momentum conservation here. (2) Evaluate the speed of the rocket measure by inertial observer on the ground as a function of time v(t) if the speed of the gas propulsion with respect to the rocket is vret and the burning rate is constant constant! dm dt (3) Plot v(t) that you obtained from point (2) above, for three different values of gravitational field (assuming similar initial mass), which is: Imoon = 1.62 m/s? • Gearth = 9.81 m/s? Ijupiter = 24.79 m/s? in a single plot, if the burn dm ate is constant = 1500 kg/s. Analyze your result and dt describes how the speed increases for each situation! 20:18 Ai 11/03/2022

when we calculate escape speeds, we usually do so with the assumption that the object from which we are calculating escape speed is isolated. This is, of course, generally not true in the solar system. Show that the escape speed at a point near a system that consists of two stationary massive spherical objects is equal to the square root of the sum of the squares of the escape speeds from each of the two objects considered individually.

A star with mass M and radius R collides head-on with another star of mass ¾*M and radius 4/5*R, and they coalesce to form a new start at rest whose radius is 6/5*R. Assume that initially the colliding stars had angular velocities with opposite directions but the same magnitude w. What is the magnitude and direction of the final’s stars angular velocity? (Express the magnitude as a fraction of w.)