Consider the motion of a buillet that is fired from a rifle 2 m above the ground

Question

Consider the motion of a buillet that is fired from a rifle 2 m above the ground in a northeast direction. The initial velocity of the bullet is (100,100,0). Assume the x points east, the y-axis points north, the postive z-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the object a. Find the velocity and position vectors for t20. b. Make a sketch of the trajectory c.Determine the time of flight and range of the bullet. d. Determine the maximum height of the bulet a. The velocity vector is vt)UL Simplity your answers. Use integers or decimals for any numbers in the expressions.) The position vector is r(t)- (Simplity your answers. Use integers or decimals for any numbers in the expressions.) b. Choose the correct sketch below. O A B. O c. C. The time of flight is s. (Type an integer or decimal rounded to three decimal places as needed.) The range ism.

Explanation / Answer

From the given question,

a) velocity vector is v(t) = 100i + 100j + (gt) k

position vector r(t)= 100t i + 100t j + (1/2)gt^2 k

b)correct answer is option(c).

this is because, the only force acting is gravity. so, body will go in parabolic path with decreasing height.

c) time of flight:

2= (1/2)gt^2

t=sqrt(2*2/9.8)

=0.639 s

range= sqrt[(100*0.64 )^2+ (100*0.64 )^2]

=90.5 m in north east direction.

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