A body is to be projected at an angle with a velocity 24m/s just to pass over an obstacle 14m high at adistance of24m.then angle is what.

To determine the angle at which the body should be projected, we can use the principles of projectile motion. Here's how you can solve the problem step by step:

Step 1: Split the given information into horizontal and vertical components:
Given:
Initial velocity (u) = 24 m/s
Distance to be covered (range) = 24 m
Height of obstacle (h) = 14 m

Horizontal Component:
Since there is no external force acting horizontally, the initial horizontal velocity (u_x) remains constant throughout the motion. Therefore, the horizontal component is the range:
Horizontal component (u_x) = range = 24 m

Vertical Component:
The vertical motion is affected by gravity. We can use the equations of motion to find the vertical component (u_y).

Let's consider the vertical motion when the body is at its maximum height, just over the obstacle:
Initial vertical velocity (u_y) at that point is 0 m/s (since it momentarily stops). The vertical displacement is equal to the height of the obstacle:
Vertical displacement (s_y) = height of obstacle = 14 m

Using the equation of motion, s_y = u_y * t + (1/2) * g * t^2, and substituting the known values:
14 m = 0 * t + (1/2) * (-9.8 m/s^2) * t^2

Simplifying the equation:
14 m = -4.9 m/s^2 * t^2

Step 2: Solve for time (t):
Rearranging the equation:
4.9 m/s^2 * t^2 = -14 m

Taking the square root of both sides:
2.21 s * t = -3.74 s

Since time cannot be negative, we can ignore the negative value:
t ≈ 1.7 s (approximately)

Step 3: Calculate the vertical component (u_y):
Using the equation of motion, v = u + gt, where v is the final velocity (which is 0 m/s at the highest point), and g is the acceleration due to gravity (-9.8 m/s^2):
v = u_y + gt

0 m/s = 0 m/s + (-9.8 m/s^2) * 1.7 s
0 m/s = -16.66 m/s

Since the vertical velocity becomes negative (-16.66 m/s), the projectile is moving downward.

Step 4: Determine the angle (θ):
To find the angle, we can use the trigonometric relationship between the horizontal and vertical components.

tangent(θ) = opposite (u_y) / adjacent (u_x)

tangent(θ) = (-16.66 m/s) / (24 m/s)
θ ≈ -0.6941 radians

To convert the angle to degrees, we can use the conversion factor: 1 radian = 180/π degrees.
θ ≈ -0.6941 * (180/π) degrees
θ ≈ -39.7 degrees

Note: The negative angle indicates that the body is projected in the downward direction.

Therefore, the angle at which the body should be projected to just pass over the obstacle is approximately 39.7 degrees downward.

Do the vertical problem first

Vi = initial speed up
then
v = Vi - g t
at top, v = 0
0 = Vi - g t
Vi = g t
t = Vi/g

h = 0 + Vi t - .5 g t^2
14 = Vi^2/g - .5 Vi^2/g
28 g = Vi^2
Vi = sqrt (28 g)
Vi = 16.6 m/s

Vi = v sin theta
16.6 = 24 sin theta
so ....