The plane of a rectangular coil, 7.2 cm by 3.7 cm, is perpendicular to the direction of a uniform magnetic field B. If the coil has 104 turns and a total resistance of 12.4 Ω, at what rate must the magnitude of B change to induce a current of 0.05 A in the windings of the coil? Answer in units of T/s.

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

Asap i'm in class rn a 1,000-kg car is traveling 20 m/s on a flat stretch of road. it gets to a hill and coasts uphill until it stops. how high up the hill does the car travel? givens: equation: 1/2mv2initial=mghfinal solve for h. plug & chug, label.

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?