Projectile Motion Tutorial Learning Goal: To understand how to apply the equatio
ID: 1545722 • Letter: P
Question
Projectile Motion Tutorial Learning Goal: To understand how to apply the equations for one- dimensional motion to the x and y directions separately in order to derive standard formulas for the range and height of a projectile. (Figure 1) A projectile is fired from ground level at time t 0, at an angle 0 with respect to the horizontal. It has an initial speed vo. In this problem we are assuming that the ground is level. Figure 1 of 1 H Part A Find the time tH takes the projectile to reach its maximum height H. Express t H in terms of vo, 0, and g (the magnitude of the acceleration due to gravity). H 10. sin (theta) /g Submit Hints My Answers Give Up Review Part Incorrect; Try Again: 6 attempts remaining Part B Find tR, the time at which the projectile hits the ground after having traveled through a horizontal distance R Express the time in terms of vo, 0, and g. 2 Va sin 0 Submit Hints My Answers Give Up Review Part Incorrect; Try Again: 6 attempts remainingExplanation / Answer
a) time to reach max height = time for vertical velocity to reach 0
v = 0 = v0*sin - g*tH
tH = v0*sin/g
b) tR = 2*tH = 2*v0*sin/g
since time to rise = time to fall (ignoring drag)
c) H = v0*sin*tH - ½g(tH)²
H = v0*sin*(v0*sin/g) - ½g(v0*sin/g)²
H = (v0*sin)² * (1/g - 1/2g)
H = (v0*sin)²/2g
d) R = v0*cos*tR = v0*cos*2*v0*sin / g
Use the trig identity 2*sin*cos = sin(2), and you get
R = v0*sin(2)/g
Hope this helps!
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.