# Tutor profile: Kevin K.

## Questions

### Subject: Physics (Newtonian Mechanics)

A ball is shot at a 30 degree angle from the horizontal with an initial velocity of 20 m/s. How far does it go in the x direction and how long does it take?

Break up velocity into x and y components. v_y^2=vo_y^2+2ay but here a is negative 9.81 (gravity) and a the top velocity is zero in the y. The y is solved for 5.096m. Use delta_y = vo*t+1/2at^2. Only unknown is the time. Solve for time and get about 1 sec. However, the ball must make the trip down and since acceleration in the y is the same, the total time is simply double (2). So it takes about 2 seconds to get to its end, but how far? Use delta_x=vo_x*t+1/2at^2 but no acceleration in the x. Solve for delta_x to get about 34.64m.

### Subject: Calculus

Find the slope of the graph f(x)=x^2+2x+sinx at pi.

slope=df/dx(pi) =2x+2+cosx =2(pi)+2+cos(pi) =2*pi+1 ~7.28

### Subject: Algebra

Find the roots for the quadratic equation: y=x^2+2x+1

y=x^2+2x+1 roots=[-b+/-sqrt(b^2-4ac)]/(2a) roots=[-2=/-sqrt(2^2-4*1*1)]/(2*2) roots=-1

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