I tried all the formulas i know but i cannot answer it I really need your help in this question..
A projectile was launched 64° above the horizontal, attaining a height of 10 m. What is the projectile's initial speed?
You can apply conservation of energy to the vertical velocity component, since the horizontal component does not change.
(Vo sin64)^2/2 = g H = 98 m^2/s^2
Vo sin64 = 196
Vo sin64 = 14
Vo = 15.6 m/s
thanks
To find the initial speed of the projectile, we can use the equations of projectile motion. The vertical motion and horizontal motion of the projectile are independent of each other, so we can solve each motion separately and then combine the results.
Let's start with the vertical motion. We know that the projectile was launched 64° above the horizontal and attained a height of 10 m. The vertical motion can be described by the equation:
y = y0 + v0y*t - (1/2)gt^2
where y is the final position (10 m), y0 is the initial position (0 m), v0y is the initial vertical velocity, t is the time, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since the initial vertical velocity is v0y = v0 * sin(θ), where θ is the launch angle (64°) and v0 is the initial speed, we can rewrite the equation as:
y = v0 * sin(θ) * t - (1/2)gt^2
Now, let's look at the horizontal motion. The horizontal motion can be described by the equation:
x = v0x * t
where x is the horizontal distance traveled by the projectile and v0x is the initial horizontal velocity. Since there is no acceleration in the horizontal direction, the horizontal velocity remains constant, and v0x = v0 * cos(θ), where θ is the launch angle (64°) and v0 is the initial speed.
We can use the time it takes for the projectile to reach the maximum height as t/2, where t is the total time of flight. At the maximum height, the vertical velocity is zero, so we can solve for t using the equation:
0 = v0 * sin(θ) - gt/2
By rearranging this equation, we can solve for t:
t = 2 * v0 * sin(θ) / g
Now, we can substitute this expression for t into the equation for the vertical motion:
10 = v0 * sin(θ) * (2 * v0 * sin(θ) / g) - (1/2)g * (2 * v0 * sin(θ) / g)^2
Solving this equation will give us the initial speed (v0) of the projectile. However, since this is a quadratic equation, it may not have a simple algebraic solution. We can solve it numerically using a graphing calculator, spreadsheet software, or an online solver.
Alternatively, you can use an online projectile motion calculator or physics software to directly input the given parameters (launch angle, height, acceleration due to gravity) and obtain the initial speed.