Using the MATLAB program above of (free fall with drag force) to answer the following questions. Show all work when needed.

A. If a raindrop falls from a cloud 2000 m above the ground, what would be the velocity when it hits the ground with no drag force? with drag force? Estimate the force of a drop hitting your head if it comes to a stop in deltat=0.1s. (Recall that F = deltap/deltat.)

V (no drag) = ____________ V(w/drag) = ____________ Force = ________________

Would this be dangerous for you to be outside?

2. If a 12 hailstone falls from a cloud 2000 m above the ground, what would be the velocity when it hits the ground with no drag force? with drag force? Estimate the force of a hail stone hitting your head if it comes to a stop in deltat=0.01s.

   V (no drag) = ____________ V(w/drag) = ____________ Force = ________________

   Would this be dangerous for you to be outside?

3. Estimate the speed of a penny dropped from the observation deck of the Empire State building when it hits the ground. Estimate the force when it hits the ground if it comes to a stop in deltat=0.01s.

Would this be dangerous for you to be outside?

V (no drag) = ____________ V(w/drag) = ____________ Force = ________________

W NP Join W NOCOJO UTILITI Eulers_Equation_example_1.m X + $ Initialize Variables Vo=4; a=9.8; dt=.1 tstart=0; tend=14; t=tstart:dt:tend; veulersvo; A=.0042; rho=1.2; C=.5; mass=. 145; for i=2: length(t) vexact (i)=v0+a*t(i); Exact Solution h(i-1)=a-(.5*A*rho*C* (veuler(i-1))^2) /mass; veuler (i)=veuler (i-1)+ h (i-1) *dt; Euler's Method end 19 20 N N LAW NA N N 1 & Plot and compare plot(t, vexact, 'b-',t, veuler, 'ro'); xlabel('Time (3)'); ylabel('Velocity (m/s)'); legend('Exact', 'Euler Method'); W NP Join W NOCOJO UTILITI Eulers_Equation_example_1.m X + $ Initialize Variables Vo=4; a=9.8; dt=.1 tstart=0; tend=14; t=tstart:dt:tend; veulersvo; A=.0042; rho=1.2; C=.5; mass=. 145; for i=2: length(t) vexact (i)=v0+a*t(i); Exact Solution h(i-1)=a-(.5*A*rho*C* (veuler(i-1))^2) /mass; veuler (i)=veuler (i-1)+ h (i-1) *dt; Euler's Method end 19 20 N N LAW NA N N 1 & Plot and compare plot(t, vexact, 'b-',t, veuler, 'ro'); xlabel('Time (3)'); ylabel('Velocity (m/s)'); legend('Exact', 'Euler Method')