The range of a Cannon ball fired horizontally from a laboratory table equals to 8/ 3 times the height of the table . what is the direction of the velocity of the projectile as it strikes the ground?
range = 8/3 max-height
range = (U^2sin2theta)/g
max height = (u^2sin^2theta)2g
so, (U^2sin2theta)/g = 8/3 (u^2sin^2theta)2g
things that cancel out cancel out like u^2 , g
and left with
sin2theta = 8/3 sin^2thea
and sin2theta = 2sin theta x cos theta from trig properties
and sin^2 theta = sin theta x sin theta
so , 2sin theta x cos theta = 8/3 sin theta x sin theta
things that cancel out again one of the sin theta, multiply both sides by 1/2
cos theta =8/6 sin theta
6/8 = sin theta/cos theta, which is tan theta
tan theta = 3/4
to find the angel just plug the inverse of tan theta in ur calculator it will turn out to be
37 degrees. hope that helps
please work this question ?
We know that this equation is horizontal
So initial vertical velovity is equal to zero and tan theta is equal to v in y direction over v in x direction so to find v in x direction
X=v in x times the time
X=8/3h given
So, v in x=x/t
And we don't have time so we need to find it usin another equation in x or y time is the same so,
Y=ut+1/2at^2. But u is zero so
Y=1/2at^2
t=√2h/g
So when we plug it in to the equation
Vx=x/√2h/g=8/3h×√2h/g
So, we need to find the value of v in y direction so,
V=u+gt, but u is zero, V=gt
V=g×√2h/g
Ao now we have both values so,
Tan theta=8/3h×√2h/g the whole over
g×√2h/ when we divide those values we get tan theta=6h/8h, h cancel out. So the answer is tan invers(3/4) you can check it on your mobile 36.6... Which is rounded to be 37°
Girma
Well, you know what they say about cannonballs fired horizontally - they never seem to have a sense of direction! When the cannonball strikes the ground, its velocity will be downward. It's just like when I try to walk before I've had my coffee - I tend to fall down too!
To determine the direction of the velocity of the projectile as it strikes the ground, we can use the concept of projectile motion. When a cannonball is fired horizontally, it only has an initial horizontal velocity and no initial vertical velocity.
The range of a projectile fired horizontally can be determined using the equation:
Range = (Initial horizontal velocity) * (Time of flight)
In this case, we are given that the range of the cannonball is equal to 8/3 times the height of the table. Let's call the height of the table "h."
So, Range = 8/3 * h.
On the other hand, the time of flight of the projectile can be calculated using the formula:
Time of flight = (2 * Initial vertical velocity) / (acceleration due to gravity)
Since the cannonball is fired horizontally, it has no initial vertical velocity. Therefore, the time of flight is zero.
Plugging in the values into the equation Range = (Initial horizontal velocity) * (Time of flight), we get:
8/3 * h = (Initial horizontal velocity) * (0)
Since the time of flight is zero, we can conclude that the initial horizontal velocity is also zero.
When the cannonball strikes the ground, its velocity will be entirely vertical in the downward direction due to the acceleration caused by gravity. Thus, the direction of the velocity of the projectile as it strikes the ground is downward or vertically downward.