Question

A crossbow is aimed horizontally at a target 36 m away. The arrow hits 37 cm below the spot at which it was aimed. What is the initial velocity of the arrow? v0​=m/s A proton in a synchrotron is moving in a circle of radius 1 km and increasing its speed by v(t)=c1​+c2​t2 , where c1​=2.6×105 m/s and c2​=105 m/s3.

a. What is the proton's total acceleration at t=5.0 s ? a=×109 m/s2
b. At what time does the expression for the velocity become unphysical? t=s Raindrops fall vertically at 4.5 m/s relative to the earth.
What does an observer in a car moving at 21.5 m/s in a straight line measure as the speed of the raindrops?

Answer 1

The initial velocity of the arrow can be found using the principles of projectile motion. The initial velocity of the arrow is approximately 127.66 m/s.

Step-by-step explanation:

The initial velocity of the arrow can be found using the principles of projectile motion. When a projectile is launched horizontally, the vertical motion is affected by gravity while the horizontal motion remains constant. The arrow hits 37 cm below the spot it was aimed, which indicates that it falls vertically due to the force of gravity. Using the formula for the vertical displacement, we can solve for the initial velocity.

Let's assume the initial velocity of the arrow is v0 and its time of flight is t. The vertical displacement can be calculated using the equation:

h = (1/2)gt²

Where h is the vertical displacement (37 cm = 0.37 m) and g is the acceleration due to gravity (-9.8 m/s²). Solving for t, we get:

t = sqrt((2h)/g)

Substituting the values, t = sqrt((2 * 0.37) / -9.8) = 0.282 s

The horizontal distance traveled by the arrow can be calculated using the equation:

d = v0 * t

Substituting the values, 36 m = v0 * 0.282 s

Solving for v0, v0 = 36 / 0.282 = 127.66 m/s

Therefore, the initial velocity of the arrow is approximately 127.66 m/s.