First pic info, second pic questions webassign. The Expert TAI Human-like Gradin

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First pic info, second pic questions webassign. The Expert TAI Human-like Grading, Automatedl 40 m/s degrees Time 000 sec fire reset Display in a New Window Explore A projectile is launched with a launch angle of 70 with respect to the horizontal direction and with an initial speed of 12 m/s. (A) How do the vertical and horizontal components of the projectile's velocity vary with time? (B) How long does it remain in flight? For a given launch speed, what launch angle produces the longest time of flight? Consider the projectile to be a point mass that starts with an initial velocity, upward and to the right, with forces from air resistance neglected. There is no force acting horizontally to accelerate its horizontal motion, while its vertical motion is accelerated downward by gravity. Therefore, as the projectile moves to the right at a constant rate, the vertical part of its motion consists of first rising upward and then moving downward until the projectile strikes the ground. Use the simulation to display the projectile motion. The velocity has components in both the x- and y directions, so we categorize this as a problem involving particle motion in two dimensions. The particle also has only a y component of acceleration, so we categorize it as a particle under constant acceleration in the y direction and constant velocity in the x- Analyze (A) How do the vertical and horizontal components of the projectile's velocity vary with time? The initial velocity in the x-direction vro is related to the initial speed by

Explanation / Answer

Given,

theta = 70 degrees

speed = 12m/s

: Vxo = Vo* cos70 = 12*cos 70 = 4.104 m/s

x = xo + vxo*t = 0 +  4.104[m/s] *t

V yo = vo*sin 70 = 11.276 m/s

y = y0+vyo*t - 0.5*gt^2 = 0 + 11.276 [m/s] *t - 4.9 [m/s^2] *t^2

===========================================

B)

t(flight) = 2*Vyo / g = 2*11.276 / 9.8 = 2.310 [s]

===========================================

c) angle is

T(flight) = 2*Vi*sin(theta)/g

equating to 0 and diff w.r.t to theta

2*Vi/g*cos(theta) = 0

theta=90 [degrees]

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