How Long Does It Take for a Projectile to Hit the Ground?

[needhelp83]

1.) A projectile is shot from the edge of a cliff 125 m above ground level with an initial
velocity of 105 m/s at an angle of 37o with the horizontal.
Determine:
a) the time it takes for the projectile to hit the ground
b) the distance traveled by the projectile as measured from the base of the cliff
c) find the horizontal and vertical components of the projectile's velocity the instant
before hitting the ground
d) the magnitude of the velocity
e) the angle made by the velocity vector with the horizontal.




Horizontal
s = ?
u = 105cos37 = 83.8567 m/s
v = "
a = 0
t = ?

Vertical
s = -125 m
u = 105sin37 = 63.1906 m/s
v = ?
a = -9.8 m/s/s
t = ?

Use:
v2 = u2 + 2as
v2 = (63.1906 m/s)2 + 2(-9.8 m/s/s)(-125 m)
|v| = 80.2686 m/s but v must be going down so
v = -80.2686 m/s

A) v = u + at
-80.2686 m/s = 63.1906 m/s + (-9.8 m/s/s)t
t = 14.6387 s = 14.6 s

B)
vav = s/t
83.8567 m/s = s/14.6387 s
s = 1227.5528 m = 1230 m or 1.23 km

C)
when it hits the ground the velocity components are:
83.8567 m/s x + -80.2686 m/s y or 83.9 m/s x + -80.3 m/s y (c)

D)
This has a magnitude of
(83.85672 + 80.26862)1/2 = 116.08 m/s = 116 m/s (d)

E)
Which forms an angle of
tan-1(80.2686/83.8567) = 43.7o below the horizontal (e)

 

[gunblaze]

Yup. All are correct.

D) This has a magnitude of
(83.85672 + 80.26862)1/2 = 116.08 m/s = 116 m/s (d)

Maybe you could perhaps elaborate how u arrive at this answer. The answer is right but the working seems a little wrong.

 

[kyle8921]

Overall, the projectile will hit the ground at approximately 14.6 seconds, after traveling a distance of 1.23 km. Its velocity before hitting the ground will have a magnitude of 116 m/s and will form an angle of 43.7 degrees below the horizontal. These calculations are based on the assumption of no air resistance. In real-world scenarios, air resistance would affect the trajectory of the projectile and alter the results.