A 500 kg rocket sled is sitting at rest at the bottom of a r…

A 500 kg rocket sled is sitting at rest at the bottom of a ramp (i.e., ground level, y = 0 m).  It has just enough fuel to accelerate along the length of the ramp.  The sled is propelled along a 25 m long ramp of angle θ = 30˚ with a constant acceleration.   When it leaves the ramp, the engine cuts off and it has a speed of 948.7 m/s. Once the sled leaves the ramp, it travels as a projectile through the air. (25 points)   a) Find the height of the ramp. height = [rampheight] b) Find the velocity vector of the sled at the instant it leave the ramp.  Give the velocity in terms of the x- and y- coordinate system shown. v = [xcomponent] + [ycomponent]   c) What is the thrust provided by the rocket engine? Thrust = [thrustforce] d) What is the total time the sled is in the air? Time of Flight = [flighttime] e) When the sled lands, how far has it traveled horizontally from the end of the ramp? xdistance = [horizontaldistance]

A conducting rod of length ℓ= 25 cm is placed on a U-shaped…

A conducting rod of length ℓ= 25 cm is placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of 8.0 Ω, as shown in the figure. The wire and the rod are in the plane of the page. A constant uniform magnetic field of strength 0.40 T is applied perpendicular to and into the paper. An applied external force pulls the rod to the right with a constant speed of 6.0 m/s. What is the magnitude of the emf induced in the rod?  

Bud’s Concert Hall hires bands to play on one-week contracts…

Bud’s Concert Hall hires bands to play on one-week contracts through an agent-booker-representation firm. A typical contract would cost Bud a fixed fee to the band and a percentage of the ticket sales.   Specifically, the contract would have Bud’s profit for a week be 90% of tickets minus a $2,000 fixed fee.  So, out of the price of a ticket, Bud gets 90% and the band gets 10%. Occasionally, Bud has the opportunity to keep a band for a second week.   If Bud keeps the band for a second week, Bud’s profit will be 60% of tickets minus a $2,000 fixed fee.  So, Bud keeps a bit less of the ticket sales in the second week of an old band. Bud should switch to a new band if Bud expects the new band to sell