In Postdam in 1988, Petra Felke of E. Germany set a woman's world record by throwing a javelin
Assuming it was launched at a 40 degree angle to the horizontal 6.5 ft above the ground, what was the javelin's initial speed
How high did the havelin go?
We never went over how to find the initial anything in class, so once i get that I am all set
The initial values are used to determine in the constants of integration when solving the fundamental differential equations governing the object's motion. Treating the object like a point mass, the 4 equations governing the motion are:
1) v_h = d(s_h)/dt
2) a_h = d(v_h)/dt
3) v_v = d(s_v)/dt
4) a_v = d(v_v)/dt
where:
"t" is time in sec (t=0 at start),
"v_h" the object's horizontal (component) velocity in (m/sec),
"v_v" the object's vertical (component) velocity in (m/sec),
"s_h" its horizontal distance from a reference 0 point (in m),
"s_v" its vertical distance from ground (in m),
"a_h" its horizontal (component) acceleration owing to gravitational force, which is a constant zero (0 m/sec^2) in this case.
"a_v" its vertical (component) acceleration owing to gravitational force, which is a constant (-9.8 m/sec^2) in this case.
The equations are integrated in pairs (#1/2 and #3/4). We use the first pair as an example and drop the subscripts for notational simplicity.
Integrating Eq #2 first yields (since "a" is constant):
Integrating Eq #2 -----> a*t = v - v_0
where v_0 is the initial velocity. Solving for "v" in the above result, subbing into Eq #1, and integrating yields:
Subbing into Eq #1 -----> (a*t + v_0) = ds/dt
Integrating Eq #1 -----> (1/2)*a*(t^2) + (v_0)*t = s - s_0
where s_0 is the initial position (in m). The total result of integrating both pairs will be 4 equations (#5-8) which can be used in various combinations to solve the problem:
Eq #5 -----> v_h = (a_h)*t + v_h_0
Eq #6 -----> v_v = (a_v)*t + v_v_0
Eq #7 -----> s_h = s_h_0 + (v_h_0)*t + (1/2)*(a_h)*(t^2)
Eq #8 -----> s_v = s_v_0 + (v_v_0)*t + (1/2)*(a_v)*(t^2)
These are subject to the following conditions:
s_v = 0 when object hits ground
s_h = (262 ft 5 in.) = (???? meters) when object hits ground
v_v_0 = (v_h_0)*tan(40 deg)
initial speed V_0 = sqrt( (v_v_0)^2 + (v_h_0)^2 )
max height occurs when v_v = 0 meters
a_v = -9.8 m/sec^2
a_h = 0 m/sec^2
Use the above equations and conditions to solve the problem.
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