Question

Мяч, брошенный под некоторым углом к горизонту с начальной скоростью 10 м/c, через 0,5 с имел скорость 7 м/c. Определите максимальную высоту подъема мяча и время полета всего движения.

Answer 1

Vy=V0*sina-g*t     Vx=V0*cosa   V^2=Vx^2+Vy^2
V^2=V0^2+g^2*t^2-2*(V0*sina)*g*t
sina==(V0^2+g^2*t^2-V^2)/2*V0*g*t=(100+100*0,25-49)/2*10*10*0,5=0,76
Hmax=V0^2*sin^2a/2*g=100*0,76^2/2*10=2,89 м
t=2*V0*sina/g=2*10*0,76/10=1,52 c

Answer 2

Calculation of Maximum Height and Total Flight Time

To determine the maximum height and total flight time of a ball thrown at an angle to the horizon with an initial velocity of 10 m/s and a velocity of 7 m/s after 0.5 seconds, we can use the equations of projectile motion.

The maximum height can be calculated using the formula:

h = (v^2 * sin^2θ) / (2 * g)

where: - h is the maximum height - v is the initial velocity (10 m/s) - θ is the angle of projection - g is the acceleration due to gravity (approximately 9.8 m/s^2)

The total flight time can be calculated using the formula:

t = (2 * v * sinθ) / g

where: - t is the total flight time - v is the initial velocity (10 m/s) - θ is the angle of projection - g is the acceleration due to gravity (approximately 9.8 m/s^2)

Let's calculate the maximum height and total flight time.

Using the given information, we know that the velocity after 0.5 seconds is 7 m/s. We can use this information to find the angle of projection.

From the equation v = u + gt, where u is the initial velocity, g is the acceleration due to gravity, and t is the time, we can rearrange the equation to solve for the angle of projection:

θ = arcsin((v - u) / (gt))

Substituting the values, we have:

θ = arcsin((7 - 10) / (9.8 * 0.5))

Calculating this value, we find that θ is approximately 45.58 degrees.

Now, we can substitute the values into the formulas for maximum height and total flight time:

h = (10^2 * sin^2(45.58)) / (2 * 9.8)

t = (2 * 10 * sin(45.58)) / 9.8

Calculating these values, we find that the maximum height is approximately 3.57 meters and the total flight time is approximately 1.44 seconds.

Therefore, the maximum height of the ball is approximately 3.57 meters and the total flight time is approximately 1.44 seconds.