A particle P is projected vertically upwards with speed 25 m s−1
from a point 3 m above horizontal
i) Find the time taken for P to reach its greatest height. i found the answer ,it is 2.5 s
ii)Find the length of time for which P is higher than 23 m above the ground. (how do i do this ?)
iii) P is higher than h m above the ground for 1 second. Find h.
i dont understand how to tackle these questions. :D
- NCSLv 72 months agoFavorite Answer
ii) there are a couple of routes. I would set up the quadratic describing vertical motion
h = h0 + v*t - ½gt²
and plug in the knowns:
23 m = 3m + 25m/s*t - ½*9.8m/s²*t²
4.9t² - 25t + 20 = 0
quadratic with roots at
t = 0.993 s
and t = 4.11 s
The ball is above 23 m BETWEEN these two times, or for about 3.1 seconds. ◄
You could instead find the maximum height H and then solve
H - 23m = ½gt²
for t and then double it (up then down). I'll leave that for you if you're interested.
iii) Now I think we WILL need to find the maximum height.
H = h0 + v² / 2g = 3m + (25m/s)² / 19.6m/s² = 34.9 m
If the ball was above height h for 1 second, then it was rising from h for ½ second and falling back to h for ½ second.
How far does it fall from H in ½ second?
y = ½gt² = ½ * 9.8m/s² * (0.5s)² = 1.225 m
h = 34.9m - 1.23 m = 33.7 m ◄
Hope this helps!
- Anonymous2 months ago
i) find the time t taken for P to reach its greatest height
time t = Voy/g = 25/9.806 = 2.549 sec
ii) find the time t' for which P is higher than 23 m above the ground
up time tu :
(23-ho) = 25*tu-4.903t^2
tu = (25-√
25^2-4.903*4*(23-3) ) / 9.806 = 0.994 sec
Δtu = t-tu = 2.549-0.994 = 1.556 sec
down time td :
Hmax = ho+Voy^2/2g = 3+25^2/19.612 = 34.87 m
td = √2*(Hmax-23)/g = √2*(34.87-23)/9.806 = 1.556 sec
t' = Δtu+td = 1.556+1.556 = 3.112 sec
or more simply : t' = 2*Δtu = 1.556*2 = 3.112 sec
iii) P is higher than h'' m above the ground for t'' = 1 sec : find h''.
thanks to symmetry of the trajectory near the apex :
h'' = Hmax-g*(t''/2)^2/2 = 34.87-9.806*0.5^2/2 = 33.64 m
- 2 months ago
Ii) time taken = sq.root ( 2h/g ) = sq.root(2x23/10) = 2.144 sec
Iii) height h = 25x1+1/2x10x1= = 30m.