Subject: CALCULUS BASED PHYSICS

Please help me to answer the following (detailed and complete solution):

1.

A +10uC point charge is 25cm away from a -20uC point charge. Calculate the magnitude of the electric force between them. Use k = 9x10^9Nm^2/C^2 (10 pts)An object's acceleration is given by a = cos(2t)i + 4t j + 6sin(3t)k. The objects initial velocity is v(0)=6i + 2j + 7k and the objects initial position is r(0)=1 - 9j + 6k. Determine the object's velocity and position functions. Express in terms of vector notation and solve for its magnitude. (15 pts)Two vectors are given by, a = 2i + j + k and b= i + j + k. Find the dot product of these two vectors. (5 pts)Two vectors are given by, a = 2i + j+ k and b = i+ j + k. Find the cross product of these two vectors. (5 pts)A scuba diver is hunting for fish with a spear gun. He accidentally fires the gun so that the spear punctures the side of a cruise ship. The hole is located at a depth 10m below the water surface. What speed does the water enter the cruise ship through the hole? Use Bernoulli's Equation. (15 pts)A +100uC charge is at the origin. A - 50uC charge at x=2 and a +200uC is placed at x = -4m. Use k = 9x10^9Nm^2/C^2 (15 pts) a. What is the force acting on the +100uC charge? b. What is the force acting on the +200uC charge?A force of 500N exists between two identical point charges separated by a distance of 4cm. Calculate the magnitude of the point two charges. Use k = 9x10^9Nm^2/C^2 (15pts)