m2: projectiles and rod questions

2 questions which are annoying me.

Stone is projected at 30 degrees above the horizontal, from a point A. The highest point of its path is 12m above A. no air resis.
find the speed with which the stone is projected from A (ans 30.7)
The stone hits a tree when it has travelled a horizontal distance of 75m.
find the angle which the direction of motion of the stone makes with the horizontal just before it hits the tree. (ans 24.9)

The end A of a uniform rod AB, of length 30cm and weight 13N, is freely hinged at a fixed point. One end of a light inextensible string of length 72cm is attached to the end B of the rod. The other end of the string is attached to a fixed point C, which is at the same horizontal level as A. The rod is in equilibrium with the string at right angles to the rod.
Find the tension in the string (ans 2.5)
the magnitude and direction of the force acting on rod at A. (12.2N 79.1 deg)

Thanks in advance for any help.

Reply 1

al-khwarzimi

S=75m
V horizontal =30.7 cos 30= 26.56
so t when s is 75m = 75/26.56 = 2.82
s takes only 1.56 sec to go to 12m vertical height so it has spent 1.26 sec coming back to horizontal
hence v vertical = u (speed at top height i.e 12m =0) + 9.8x 1.26 (as t=1.26 sec)
so v vertical= 12.348
therefore tan x = 12.348 / 26.56
so x = 24.9 degrees QED.

Reply 2

yusufu

16

evariste

2 questions which are annoying me.

Stone is projected at 30 degrees above the horizontal, from a point A. The highest point of its path is 12m above A. no air resis.
find the speed with which the stone is projected from A (ans 30.7)
The stone hits a tree when it has travelled a horizontal distance of 75m.
find the angle which the direction of motion of the stone makes with the horizontal just before it hits the tree. (ans 24.9)

i did this from a past paper.
you have to find the vertical component of the velocity and the horizontal velocity then put the two together to find the actual velocity:

horizontally: s=75, u= 30.7cos30 (accn is 0 so speed is constant)
t=s/u = 75/30.7cos30 = 2.82s

vertically:
u=30.7sin30, a= -g = -9.8, t=2.82, v=?

v=u+at = 30.7sin30 -(9.8*2.82) = -12.29m/s

horizontal velocity = 30.7cos30 = 26.6m/s, vertical velocity = 12.29m/s (downwards)

so, using trig:
tanA = 12.29/26.6 => A = 24.9 degrees

evariste

The end A of a uniform rod AB, of length 30cm and weight 13N, is freely hinged at a fixed point. One end of a light inextensible string of length 72cm is attached to the end B of the rod. The other end of the string is attached to a fixed point C, which is at the same horizontal level as A. The rod is in equilibrium with the string at right angles to the rod.
Find the tension in the string (ans 2.5)
the magnitude and direction of the force acting on rod at A. (12.2N 79.1 deg)

Thanks in advance for any help.

this is from the same paper! :smile:

(see the force diagram attached)

Tension in the string:
Taking momenst around A:

13cosM *0.15 = T*0.30
13*5/13 *0.15 = 0.3T
0.75Nm = 0.3T
T = 2.5N

forces down = forces up
Y + TcosM = 13
Y = 13 - 2.5*5/13 = 12.03N

forces left = forces right

X = TsinM
X = 2.5*12/13
X = 2.31N

using pythahgoras on X and Y

sqrt(2.31^2 + 12.03^2) = 12.2N

using trig: tanK = 12.03/2.31
K = 79.1 degrees

Force Diagram.JPG14.0KB

Reply 3

al-khwarzimi

Undry1

i did this from a past paper.
you have to find the vertical component of the velocity and the horizontal velocity then put the two together to find the actual velocity:

horizontally: s=75, u= 30.7cos30 (accn is 0 so speed is constant)
t=s/u = 75/30.7cos30 = 2.82s

vertically:
u=30.7sin30, a= -g = -9.8, t=2.82, v=?

v=u+at = 30.7sin30 -(9.8*2.82) = -12.29m/s

horizontal velocity = 30.7cos30 = 26.6m/s, vertical velocity = 12.29m/s (downwards)

so, using trig:
tanA = 12.29/26.6 => A = 24.9 degrees

slight variation from my method however if you are weak in mechanincs undrys approcah is safest as you dont have to think about the sign to use for g
the rule is that u define velocity and then if velocity is in direction of g then its positive or vice versa

m2: projectiles and rod questions

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