Raindrop: the force on a small raindrop is f = m dv/dt = - yv- mg (in the y-direction.) a. find a substitution u(t) in terms of v(t) that gets rid of the pesky gravity term in the equation above, leaving you a formula similar (not necessarily identical) to .= y* u(t). b. take the indefinite integral of both sides of the formula. be careful with the constant(s) c; what happens to it/them when you take the exponential of both sides? c. substitute (t) back in, so you have a formula for the velocity of the raindrop as a function of time. d. assume the raindrop started from rest, v(t = 0) = 0. solve your equation for the unknown constant, so you have v(t) for all times t 0. e. what is the maximum velocity of the raindrop, vmax? f. the quantity m/y has units of time. discuss (1-2 sentences) the meaning m/y. g. how long does it take for the raindrop to reach 63% of its maximum velocity? 87.5%? 95%? give this in terms of m/y, and explain in a grammatically correct sentence with words) why i chose those specific what links them?

Two pans of a balance are 24.1 cm apart. the fulcrum of the balance has been shifted 1.33 cm away from the center by a dishonest shopkeeper. by what percentage is the true weight of the goods being marked up by the shopkeeper? assume the balance has negligible mass. answer in units of %.

Aball horizontally thrown from a cliff at 8m/s

Amass m = 74 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius r = 18.4 m and finally a flat straight section at the same height as the center of the loop (18.4 m off the ground). since the mass would not make it around the loop if released from the height of the top of the loop (do you know why? ) it must be released above the top of the loop-the-loop height. (assume the mass never leaves the smooth track at any point on its path.) 1. what is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? 2. what height above the ground must the mass begin to make it around the loop-the-loop? 3. if the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? 4. if the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (18.4 m off the ground)? 5. now a spring with spring constant k = 15600 n/m is used on the final flat surface to stop the mass. how far does the spring compress?