A spacecraft on its way to Mars has small rocket engines mounted on its hull; one on its left surface and one on its back surface. At a certain time, both engines turn on. The one on the left gives the spacecraft an acceleration component in the x direction of a = 5.10 m/s², while the one on the back gives an acceleration component in the y direction of ay = 7.30 m/s². The engines turn off after firing for 675 s, at which point the spacecraft has velocity components of vx = 3725 m/s and vy = 4060 m/s. What was the magnitude and the direction of the spacecraft's initial velocity before the engines were turned on? Express the magnitude as m/s and the direction as an angle measured counterclockwise from the +x axis. magnitude direction m/s counterclockwise from the +x-axis

The banded archerfish is a species of fish that lives in mangrove estuaries in Asia and Oceania. It has a unique and highly effective hunting strategy: it shoots an incredibly precise stream of water out of its mouth at almost ten meters per second, knocking insects and other small animals into the water from nearby branches! Pom Fbug (t) Ө = Our hero, a hungry archerfish, has spotted a big, delicious bug sitting on a branch a height ħ above the surface of the water. The archerfish can shoot its water jet at a speed of vo. The archerfish wants to knock the bug sideways off of the branch, so it decides to shoot so that its water jet is moving horizontally at the moment when it strikes the bug. The final goal of this problem is to find the horizontal distance, d, from the branch, and the angle above horizontal, 0, at which archerfish should shoot. d (a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of…

A jetliner is moving at a speed of 245 m/s. The vertical component of the plane's velocity is 40.6 m/s. Given sin e = 0.165, the angle theta is equal to: Select one: O e = 10.0° e = 9.5° e = 11.5° e = 11.0° O O

The figure below shows an object initially at point A traveling in the +x-direction. It turns in a circular path at constant speed until it is traveling in the +y-direction at point C. The quarter-circle arc from A to C is 245 m in length, and the particle moves from A to C in 38.0 s. Point B on the path is 35.0° below the x-axis. 0 35.0⁰ (a) What is the speed of the object (in m/s)? m/s Need Help? (b) What is the magnitude and direction of the acceleration when the object is at point B? (Enter the magnitude in m/s² and the direction in degrees counterclockwise from the +x-axis.) magnitude m/s² direction Read It counterclockwise from the +x-axis

Suppose that in the future humans can travel to different earth like planets within our galaxy. You take a trip to a new planet with a different gravitational acceleration than earth. To test this gravitational acceleration, you decide to drop a ball a distance of 2 meters. You measure how long it takes the ball to fall 2.0 meter multiple times and take an average. The average drop time is 0.52 seconds. What is the approximate magnitude of the gravitational acceleration of the planet (in units of m/s squared)?

How would  I begin to solve this problem? In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by y(t) = (RE3/2 + 3*(g/2)1/2 REt)2/3 where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)

A clown is juggling four balls simultaneously. Students use a video tape to determine that it takes the clown 0.9 s to cycle each ball through his hands (including catching, transferring, and throwing) and to be ready to catch the next ball. What is the minimum vertical speed the clown must throw each ball upward with?

Elon Musk’s SpaceX is proposing that commercial flights will be ready to go to the Moon in less than three years. Yusaku Maezawa, a Japanese billionaire, is seeking eight artists to join his trip to the Moon. He wants them to inspire everyone by creating artwork after they return to Earth. The acceleration due to gravity on the surface of the Moon is 16.6% of the acceleration due to gravity on Earth. To keep the artists comfortable, it is decided that as they lift off from the Moon, the acceleration they experience close to the surface of the Moon should be kept to the equivalent of 2.83 g (1?is the acceleration due to gravity on the surface of the Earth). What is the maximum thrust that one of the new rockets from Part 2 can withstand under this condition? Note: The weight of the artists is negligible compared to the weight of the rocket (given in part 2), so you can ignore it in your calculations!

On a spacecraft, two engines are turned on for 908 s at a moment when the velocity of the craft has x and y components of v0x = 5150 m/s and v0y = 6290 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 2.85 x 106 m and y = 4.72 x 106 m. Find the (a) x and (b) y components of the craft's acceleration

3. A small object moves on a circle of radius R = 7.87 m. The speed of the object as a function of time is v = c1*t, where c1 = 4.84 m/s². %3D → t=0 R a. The object starts at t = 0 on the positive x-axis and moves counterclockwise around the circle. When the object has an angle a = counterclockwise, what is the direction of the instantaneous velocity vector (with respect to the positive x-axis, measured counterclockwise)? 16.3 degrees with respect to the positive x-axis, measured b. What is the magnitude of the instantaneous acceleration vector at timet= 1.05s?