If a projectile is fired with an initial velocity of 500 ms

If a projectile is fired with an initial velocity of 500 m/s (meters per second) at an angle of 30 degrees above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x = 250 squareroot 3 t, y = 250t - 4.9 t^2. How far (in meters) from the gun will the object hit the ground? x = 22084 meters. x = 22073 meters. x = 21396 meters. x = 21237 meters. None of the above. Write the complex number z = 1 + 1 in polar form z = r(cos theta + f sin theta), then find z^10. Z^10 = 32i z^10 = 16i z^10 = 16 + 16i z^10 = 32 + 32i None of the above. Suppose the vectors u = and v = form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are 10 and 4 squareroot 10 10 and 2 squareroot 10 10 and 5 2 squareroot 26 and 2 squareroot 10 None of the above.

Solution

31) x = 250sqrt3t ; y = 250t - 4.9t^2

y =0 ; 250t - 4.9t^2 =0 ;

t = 250/4.9 = 51.02

x = 250sqrt3*51.02 = 22092.308

32) z= 1+i ;

in polar form z= sqrt2(cospi/4 + i*sinpi/4)

z^10 = 2^10/2( cos10pi/4) + i*sin10pi/4 )

= 32( 0 + i) = 32i

Option A